Method and Apparatus of Operating a Scanning Probe Microscope

ABSTRACT

Methods and apparatuses are provided for automatically controlling and stabilizing aspects of a scanning probe microscope (SPM), such as an atomic force microscope (AFM), using Peak Force Tapping (PFT) Mode. In an embodiment, a controller automatically controls periodic motion of a probe relative to a sample in response to a substantially instantaneous force determined, and automatically controls a gain in a feedback loop. A gain control circuit automatically tunes a gain based on separation distances between a probe and a sample to facilitate stability. Accordingly, instability onset is quickly and accurately determined during scanning, thereby eliminating the need of expert user tuning of gains during operation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.15/057,963, filed on Mar. 1, 2016 (and issued as U.S. Pat. No. 9,810,713on Nov. 7, 2017), which is a divisional of U.S. patent application Ser.No. 14/172,710, filed on Feb. 4, 2014 (and issued as U.S. Pat. No.9,274,139 on Mar. 1, 2016), which is a divisional of U.S. patentapplication Ser. No. 12/958,323, filed on Dec. 1, 2010 (and issued asU.S. Pat. No. 8,646,109 on Feb. 4, 2014), which in turn, claims priorityunder 35 USC § 1.119(e) to U.S. Provisional Patent Application No.61/265,655, filed Dec. 1, 2009. U.S. patent application Ser. No.12/958,323 is also a continuation-in-part of U.S. patent applicationSer. No. 12/618,641, filed on Nov. 13, 2009 (and issued as U.S. Pat. No.8,739,309 on May 27, 2014), which in turn, claims priority under 35 USC§ 1.119(e) to U.S. Provisional Patent Application No. 61/114,399, filedNov. 13, 2008, all of which are entitled Method and Apparatus ofOperating a Scanning Probe Microscope. The subject matter of theseapplications is hereby incorporated by reference in their entirety.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention is directed to scanning probe microscopes (SPMs),including atomic force microscopes (AFMs), and more particularly, to amode of AFM operation that provides force control at high speed, lowtip-sample interaction forces and high resolution.

Description of Related Art

Scanning probe microscopes (SPMs), such as the atomic force microscope(AFM), are devices which typically employ a probe having a tip and whichcause the tip to interact with the surface of a sample with low forcesto characterize the surface down to atomic dimensions. Generally, theprobe is introduced to a surface of a sample to detect changes in thecharacteristics of a sample. By providing relative scanning movementbetween the tip and the sample, surface characteristic data can beacquired over a particular region of the sample, and a corresponding mapof the sample can be generated.

A typical AFM system is shown schematically in FIG. 1. An AFM 10 employsa probe device or assembly 11 including a probe 12 having a cantilever15. A scanner 24 generates relative motion between the probe 12 and asample 22 while the probe-sample interaction is measured. In this way,images or other measurements of the sample can be obtained. Scanner 24is typically comprised of one or more actuators that usually generatemotion in three mutually orthogonal directions (XYZ). Often, scanner 24is a single integrated unit that includes one or more actuators to moveeither the sample or the probe in all three axes, for example, apiezoelectric tube actuator. Alternatively, the scanner may be aconceptual or physical combination of multiple separate actuators. SomeAFMs separate the scanner into multiple components, for example an XYactuator that moves the sample and a separate Z-actuator that moves theprobe. The instrument is thus capable of creating relative motionbetween the probe and the sample while measuring the topography or someother property of the sample as described, e.g., in Hansma et al. U.S.Pat. No. RE 34,489; Elings et al. U.S. Pat. No. 5,266,801; and Elings etal. U.S. Pat. No. 5,412,980.

Notably, scanner 24 often comprises a piezoelectric stack (oftenreferred to herein as a “piezo stack”) or piezoelectric tube that isused to generate relative motion between the measuring probe and thesample surface. A piezo stack is a device that moves in one or moredirections based on voltages applied to electrodes disposed on thestack. Piezo stacks are often used in combination with mechanicalflexures that serve to guide, constrain, and/or amplify the motion ofthe piezo stacks. Additionally, flexures are used to increase thestiffness of actuator in one or more axis, as described in applicationSer. No. 11/687,304, filed Mar. 16, 2007, entitled “Fast-Scanning SPMScanner and Method of Operating Same.” Actuators may be coupled to theprobe, the sample, or both. Most typically, an actuator assembly isprovided in the form of an XY-actuator that drives the probe or samplein a horizontal, or XY-plane and a Z-actuator that moves the probe orsample in a vertical or Z-direction.

In a common configuration, probe 12 is often coupled to an oscillatingactuator or drive 16 that is used to drive probe 12 to oscillate at ornear a resonant frequency of cantilever 15. Alternative arrangementsmeasure the deflection, torsion, or other characteristic of cantilever15. Probe 12 is often a microfabricated cantilever with an integratedtip 17.

Commonly, an electronic signal is applied from an AC signal source 18under control of an SPM controller 20 to cause actuator 16 (oralternatively scanner 24) to drive the probe 12 to oscillate. Theprobe-sample interaction is typically controlled via feedback bycontroller 20. Notably, the actuator 16 may be coupled to the scanner 24and probe 12 but may be formed integrally with the cantilever 15 ofprobe 12 as part of a self-actuated cantilever/probe.

Often, a selected probe 12 is oscillated and brought into contact withsample 22 as sample characteristics are monitored by detecting changesin one or more characteristics of the oscillation of probe 12, asdescribed above. In this regard, a deflection detection apparatus 25 istypically employed to direct a beam towards the backside of probe 12,the beam then being reflected towards a detector 26, such as a fourquadrant photodetector. The deflection detector is often an opticallever system such as described in Hansma et al. U.S. Pat. No. RE 34,489,but may be some other deflection detector such as strain gauges,capacitance sensors, etc. The sensing light source of apparatus 25 istypically a laser, often a visible or infrared laser diode. The sensinglight beam can also be generated by other light sources, for example aHe—Ne or other laser source, a superluminescent diode (SLD), an LED, anoptical fiber, or any other light source that can be focused to a smallspot. As the beam translates across detector 26, appropriate signals areprocessed by a signal processing block 28 (e.g., to determine the RMSdeflection of probe 12). The interaction signal (e.g., deflection) isthen transmitted to controller 20, which processes the signals todetermine changes in the oscillation of probe 12. In general, controller20 determines an error at Block 30, then generates control signals(e.g., using a PI gain control Block 32) to maintain a relativelyconstant interaction between the tip 17 and sample 22 (or deflection ofthe lever 15), typically to maintain a setpoint characteristic of theoscillation of probe 12. The control signals are typically amplified bya high voltage amplifier 34 prior to, for example, driving scanner 24.For example, controller 20 is often used to maintain the oscillationamplitude at a setpoint value, A_(S), to insure a generally constantforce between the tip and sample. Alternatively, a setpoint phase orfrequency may be used. Controller 20 is also referred to generally asfeedback where the control effort is to maintain a constant target valuedefined by setpoint.

A workstation 40 is also provided, in the controller 20 and/or in aseparate controller or system of connected or stand-alone controllers,that receives the collected data from the controller and manipulates thedata obtained during scanning to perform data manipulation operatingsuch as point selection, curve fitting, and distance determiningoperations. The workstation 40 can store the resulting information inmemory, use it for additional calculations, and/or display it on asuitable monitor, and/or transmit it to another computer or device bywire or wirelessly. The memory may comprise any computer readable datastorage medium, examples including but not limited to a computer RAM,hard disk, network storage, a flash drive, or a CD ROM.

AFMs may be designed to operate in a variety of modes, including contactmode and oscillating mode. Operation is accomplished by moving thesample and/or the probe assembly up and down relatively perpendicular tothe surface of the sample in response to a deflection of the cantileverof the probe assembly as it is scanned across the surface. Scanningtypically occurs in an “x-y” plane that is at least generally parallelto the surface of the sample, and the vertical movement occurs in the“z” direction that is perpendicular to the x-y plane. Note that manysamples have roughness, curvature and tilt that deviate from a flatplane, hence the use of the term “generally parallel.” In this way, thedata associated with this vertical motion can be stored and then used toconstruct an image of the sample surface corresponding to the samplecharacteristic being measured, e.g., surface topography. In onepractical mode of AFM operation, known as TappingMode™ AFM (TappingMode™is a trademark of the present assignee), the tip is oscillated at ornear a resonant frequency of the associated cantilever of the probe, orharmonic thereof. A feedback loop attempts to keep the amplitude of thisoscillation constant to minimize the “tracking force,” i.e., the forceresulting from tip/sample interaction, typically by controllingtip-sample separation (a controlled distance between the probe andsample). Alternative feedback arrangements keep the phase or oscillationfrequency constant. As in contact mode, these feedback signals are thencollected, stored and used as data to characterize the sample.

Regardless of their mode of operation, AFMs can obtain resolution downto the atomic level on a wide variety of insulating or conductivesurfaces in air, liquid or vacuum by using piezoelectric scanners,optical lever deflection detectors, and very small cantileversfabricated using photolithographic techniques. Because of theirresolution and versatility, AFMs are important measurement devices inmany diverse fields ranging from semiconductor manufacturing tobiological research. Note that “SPM” and the acronyms for the specifictypes of SPMs, may be used herein to refer to either the microscopeapparatus or the associated technique, e.g., “atomic force microscopy.”

As with most measuring devices, AFMs often require a trade-off betweenresolution and acquisition speed. That is, some currently available AFMscan scan a surface with sub-angstrom resolution. These scanners arecapable of scanning only relatively small sample areas, and even then,at only relatively low scan rates. Traditional commercial AFMs usuallyrequire a total scan time typically taking several minutes to cover anarea of several microns at high resolution (e.g. 512×512 pixels) and lowtracking force. The practical limit of AFM scan speed is a result of themaximum speed at which the AFM can be scanned while maintaining atracking force that is low enough not to damage or cause minimal damageto the tip and/or sample. Great strides have been made in this area inwhich SPM has achieved video scan rates with high resolution for smallsamples and small scan sizes.

Nonetheless, given current limitations associated with known modes ofoperation, including both TappingMode′ AFM and contact mode,improvements have been desired. Again, in contact mode, lateral scanningof the tip creates large forces between the tip and sample that cancompromise both. And when imaging soft samples such as biologicalsamples and polymers, the surface can be destroyed, rendering themeasurement useless, or at least deformed severely, therebysignificantly compromising resolution. Note that “imaging” is usedherein to indicate obtaining SPM data at multiple points of a samplesurface, typically by providing relative scanning motion between thesample and probe and correspondingly interacting the sample and probe.

TappingMode™ AFM is a lower force technique and is the most widely usedmode of AFM operation to map sample surfaces, especially for delicatesamples. The typical force of the tip on the sample is about a few nN totens of nN. Again, by oscillating the tip, rather than dragging the tip,the shear forces are minimized. That said, TappingMode™ AFM suffers froma drawback in that it is difficult to control the normal force acting onthe sample surface. The user typically tries to select a setpoint thatis only a small variation from the free air deflection/amplitude of theprobe in order to minimize tip-sample interaction forces to get the bestreproduction of the sample profile. The dilemma, especially for softsamples, is that if the imaging force is too low, the tip will not trackthe sample properly (i.e., maintain interaction with the sample duringthe scan), while if too high, damage/deformation of the sample may leadto an image that does not accurately reflect surface topography.Overall, the better this force can be controlled (i.e., the lower it canbe maintained) the less chance of sample and/or tip damage, and thusresolution can be improved.

A review of the tip-sample forces in each of these modes providesinsight in to the limitations of each. When a probe interacts with thesurface through TappingMode′ AFM or Jumping Mode™ (see, e.g., U.S. Pat.Nos. 5,229,606, 5,266,801 and 5,415,027, the entirety of which areincorporated by reference herein), the tip touches the surfaceperiodically. FIG. 2A illustrates the physical process within one period“T” of the tip motion. FIG. 2A shows tip trajectory in reference to thesample surface position. FIG. 2B shows the corresponding interactionforce at the same time for tip trajectory at various positions. At thepeak positions A_(max), the tip is farthest from the sample surface andnot interacting with the sample. As the tip continues to move downtoward the horizontal axis (zero tip-sample separation) it willexperience a near-field van der Waals force, F_(a) _(_) _(vdw), causingthe tip to snap into contact with the sample through van der Waalsattraction. After touching the sample, the tip remains in repulsiveinteraction for time zone δT. During this time, the tip is continuouslycontacting the sample. The positions below zero represent that the tipmay have deformed the sample, causing its position to be shown below thesample surface.

As the tip departs the surface after δT, an attractive force willdevelop a capillary meniscus, exhibiting a maximum adhesion force F_(a)_(_) _(max) right before the meniscus is broken away. The tip thenenters into a non-interactive region and continues to a maximumdeparture position.

In the interaction free zone, when the probe is farther from thesurface, the interaction force is zero or sufficiently near zero to forma baseline, as indicated in FIG. 2B. In FIG. 2B, the force above thehorizontal axis is repulsive while those points below the horizontalaxis represent a net attractive or adhesive force. The maximum repulsiveforce F_(r) _(_) _(max) usually corresponds to the lowest or smallesttip position or separation relative to the sample surface.

In prior known modes disclosed in TappingMode™ AFM and JumpingMode™ AFM,the amplitude A_(max) or RMS of the tip oscillation amplitude is used asthe feedback control parameter. An example of such feedback controlapparatus is shown in FIG. 1.

In conventional control, typically implemented using a gain controlfeedback loop, positioning actuators and a cantilever response detectioncomponent (quadrant photodetector, for example), the AFM uses detectedprobe deflection or an RMS signal corresponding to cantilever (i.e.,probe) motion as an indication of the tip-surface interaction and usesthe feedback loop to maintain constant or RMS deflection.

Yet a major limitation of conventional AFM is its inability to acquirequantitative mechanical property information simultaneously with thehigh-resolution imaging. AFM has been primarily focused on topographicalimaging. Little progress has been made in achieving quantitativemechanical mapping, including elasticity, plasticity, and work ofadhesion.

Moreover, TappingMode™ control uses amplitude or phase of the measureddeflection signal to control tip-surface interaction using feedback.Notably, both amplitude and phase are average properties of theprobe/tip oscillation using at least one cycle of interaction. Morespecifically, the average pertains to probe/sample interactionsoccurring in all the positions in the tip trajectory (FIG. 2).Therefore, there is no possibility for the control feedback to be basedon substantially instantaneous tip-sample interaction. Note thatinstantaneous interaction here refers to any point (for example, withintwo microseconds) of interaction in FIG. 2B (discussed further below).

In addition, it is important to note that TappingMode™ AFM was createdto overcome what is known as the stick-in condition that occurs whenprobe touches the sample intermittently. As the probe touches thesample, capillary force will tend to catch the tip and prevent it fromreleasing. The amplitude of probe oscillation in TappingMode™ will dropto zero, thereby causing feedback oscillation. This problem was overcomewhen using TappingMode™ by using probes having a certain stiffness,usually 10 N/m (Newton/meter) to 60 N/m, with a nominal value of 40 N/m,while operating the TappingMode™ AFM at an oscillation amplitude higherthan about 10 nm peak-to-peak. Under these conditions, as the probetouches surface, the kinetic energy of the tapping probe converts toenough static elastic energy to overcome the capillary force, assuringsteady amplitude in each cycle. One drawback of this mode is that thekinetic energy stored in the probe is also proportional to thecantilever spring constant. When employing a lower spring constantcantilever, such as 1 N/m, TappingMode™ is impossible when measuringmany materials because the cantilever can not overcome the capillaryadhesion forces using its own resonance oscillation energy.Consequently, most TappingMode™ applications are only possible when oneuses a stiff cantilever generally know in the art as a lever.

In an alternate mode of operating an SPM, known as the pulsed-force modeor PFM (see, e.g., U.S. Pat. No. 6,880,386 and U.S. Pat. No. 7,129,486),the amplitude of the oscillation of the probe is adjusted so the tipgoes in and out of contact during each cycle. In this mode, control isprovided by monitoring tip-sample interaction forces. It operates basedon properties associated with a force curve, another common measurementmade in the AFM field to measure material properties at a particularlocation. Force measurements are common, and can be mapped over anentire sample to create what is known as a force-volume image.

In PFM, by analyzing the shape of the force-distance curve, and usingthe data to control the forces acting between the tip and the sample,the amount of data acquired is lessened compared to other modes of SPMoperation. Importantly, PFM typically needs to operate at F_(r) _(_)_(i) (discussed below) or the peak pulse force, which substantiallyexceeds the adhesion induced deflection, as well as coupling induceddeflections. As a result, a high repulsive force is needed as a controlreference. Such high force could damage the sample or the tip, and thusprevent acquisition of high resolution images. Moreover, PFM has otherlimitations, particularly with respect to operating speed and resolutionlimitations, and thus, though it has been implemented to image softsamples, it has not been more widely adopted for all types of AFMimaging applications. In addition, imaging in a fluid environmentpresents a further challenge to PFM since viscous force in fluidproduces large deflection even when the cantilever probe is notinteracting with the sample.

More particularly, a main reason why imaging speed is limited instandard PFM AFM is illustrated in FIG. 2C. FIG. 2C is a graph oftip-sample interaction force versus time. The interaction force isplotted as snap-to-contact at “A”, at which point repulsive force(sample on tip) initiates at “B.” Peak repulsive force occurs at about“C” as adhesive forces pull on the tip until about point “D”, the pointat which the tip releases from the sample. Point E represents thedeflection peak of the cantilever probe when it departs from the sample.Points C and E both present themselves as a peak in the deflectionsignal. In order to assure that feedback controls tip-sample interactionproperly, the value of C should exceed E. In yet another constraint inPFM, a certain ring-down period (cycles of the probe oscillation at itsresonance frequency) is required before it is possible to determine thebaseline force needed to continue the scan. It is this waiting for thecantilever to “ring-down” (a free decay process, as in TappingMode™)that limits the modulation frequency, and thus scan speed. Moreparticularly, modulation frequency is significantly less than the proberesonance frequency (for example, a fifth or more below the proberesonance frequency).

In addition to the above-noted issues, setup and operation of therelatively complex and versatile AFM can be time consuming and tricky,especially for a novice AFM operator and/or a scientist or engineer notfamiliar with complex metrology equipment. For example, setup andoperating parameter values typically depend on factors such as the typeof sample material including whether it is hard or soft, conductive ornon-conductive, organic, synthetic or biological in nature, among otherthings.

In other measurement techniques such as scanning electron microscopy(SEM), a sample can readily be mounted in the instrument and a goodimage obtained with little user training or expertise. However, AFM isoften the preferred technique given its ability to make a wide range ofmeasurements including multidimensional topography and mechanicalproperties (elasticity, etc.). Nonetheless, AFM most often requiresexpert knowledge of the tool and the measurements to be made. In thisregard, the user needs to locate a position of interest, introduce thetip of the probe to the sample (by moving either the sample or theprobe). Then, once a measurement scan is initiated, the user needs tomake sure the tip tracks the sample, typically by maintaining a stablefeedback loop.

Moreover, once a measurement has been made, interpreting the dataobtained is often a challenge. In general, these can be time consumingtasks that most often require the knowledge and experience of aphysicist or electronics engineer, with the limitations attendant torelying on human judgment. Importantly, because AFM has the potentialfor wide applicability, it would be advantageous if the AFM did not relyso heavily on an expert's ability to perform. For example, given itsability to obtain unmatched material property measurements, includingmaps of samples, biologists and material science experts would morewidely employ AFM if it were easier to use. In this regard, ease of usewould be aided if the AFM and/or method of operation could minimize oreliminate the challenges associated with both a) maintaining feedbackstability while making and preparing to make measurements and b)interpreting the data obtained.

To address these issues, the fundamental challenges presented by AFM andits currently preferred operating modes were considered. Initially, withrespect to maintaining stability in known AFM modes, controlleradjustment is critical. In most current commercial systems, the usermust control both the setpoint as well as the gain (I (integral) and P(proportional)). With respect to the setpoint, control depends on themode. In contact mode, the instrument attempts to maintain constantcontact force between the tip and sample, which is relativelystraightforward. However, in the most widely used mode of AFM operation,oscillating mode or TappingMode™ AFM described above, controlling thesetpoint (tapping amplitude or phase) is complicated because, mostfundamentally, there is no straightforward relationship between thesetpoint and the tip-sample forces. The same setpoint change canindicate either high or low tip-sample interaction force, withcantilever dynamics (fundamental resonant frequency, etc.) being highlyinfluential, including with respect to imaging in varying environments(fluid v. atmosphere, for instance).

Stable and optimal feedback also requires applying appropriate gains.Generally feedback will become unstable under high gain, and will havereduced tracking capability under low gain. P and I gain are adjustedwith the user typically employing trial and error to make sure thefeedback remains stable, while also providing sufficient trackingcapability. However in TappingMode™ AFM, the feedback dynamics aregreatly influenced by setpoint, i.e., the same gain may exhibitdifferent feedback stability under different amplitude setpoint. Becausethe gains do not operate independently, the process of gain optimizationis particularly complicated.

Stable feedback also requires applying appropriate gain when a deviationin the oscillation from the setpoint is detected. The gain must beadjusted to return oscillation back to the setpoint. P and I gain areadjusted with the user typically employing trial and error to make surethe feedback remains stable. And because the gains do not operateindependently, the challenge is particularly complicated.

In response to the desire in the metrology field to have an AFM systemthat maintains stable feedback with less expert user participation,solutions have been proposed. Nonetheless, each has significantlimitations.

In Rifai and Youcef-Toumi, entitled “On automating atomic forcemicroscopes: An adaptive control approach,” as well as in Schitter etal., entitled “Fast contactmode atomic force microscopy on biologicalspecimen by model-based control,” higher order or model-basedcontrollers are employed over a standard P/I controller. Suchcontrollers are difficult to design and are inherently imperfect.Importantly, such controllers require information related to systemdynamics prior to operation.

Though they can be effective when operating the AFM in contact mode,they typically have difficulty working when the AFM is operated inTappingMode™ given that, as suggested above, system dynamics change withvarying setpoint.

In Astrom and Hagglund, a standard P/I controller is employed, but thetuning required for stable operation is automated. Astrom and Hagglundemploy simple regulators using specifications on phase and amplitudemargins. In this approach, the target system is most typically largeplants with slow time response. In particular, the time scale of theresponse is usually minutes to hours. This characteristic is essentiallyin direct contrast to an AFM system in which response time ismilliseconds and the Q of the response is high (low energy dissipation).In other words, automatic tuning of the controller as taught by Astromand Hagglund (using simple regulators with slow response times) wouldnot work for most AFM applications.

In another system, disclosed in Rice et al. (U.S. Pat. No. 7,513,142),the system works to detect the onset of instability, and then makes acorrection. However, because the time period between the onset ofinstability and out of control instability (i.e., instability of amagnitude requiring stopping and restarting the measurement process) isso short, it is difficult to implement control before having to stop themeasurement process. As understood in the art, hysteresis is primarilyresponsible when the system is not able to respond quickly enough.Moreover, in this solution the system makes a judgment based on themeasured oscillation. An acceptable noise amplitude is defined, and ifthat amplitude is exceeded, the system adjusts the gain. One main issueconcerns the fact that the noise amplitude is so complicated,particularly when operating the AFM in TappingMode™, and when measuringcertain types of samples. In TappingMode™ AFM, the oscillation is anon-linear representation of the interaction force between the tip andsample. Therefore, controlling the tapping amplitude, for instance,provides an indirect control of the tip-sample interaction force. Thisindirect control of the interaction force is susceptible to the effectsof variables such as oscillation harmonics and system oscillation,including from the piezo actuator itself and the mechanical componentsof the AFM. It is these Tapping Mode dynamics that make it extremelydifficult to develop a robust control algorithm, particularly whenimaging may occur in varying environments.

As a result, though this system does not require user input to make ajudgment, its ability to decipher the measured oscillation and modifythe control when the system is about to become unstable is limited.Again, in TappingMode™ AFM, system dynamics depend on both setpoint(e.g., amplitude or phase) and gain, which severely complicate theability to develop a control algorithm that can accommodateinstabilities.

In sum, while past attempts have been made with AFMs to automaticallyadjust gain, this method also has not proven particularly effective.Known methods may not be able to handle both sample topography andoperating parameters, such as setpoint, actuator hysteresis and tipshape, which can unpredictably and adversely impact any attempt tomaintain stability through gain adjustment. As a result, automatic gainadjustment is largely ineffective.

Again, this is not surprising in view of the numerous scan parametersthat must be taken into account in AFM setup and operation, along withthose that can require adjustment during AFM operation. For example, auser may need to adjust such scan control parameters as setpoint, scanspeed, proportional gain, integral gain, drive frequency, driveamplitude and other parameters. Without great care, considerableexperience, and sometimes a little luck, tip, cantilever or sampledamage can occur, poor or unusable results can be obtained, and, ininstances where everything appears to be operating well, operationalinefficiencies can be so great that scanning time is nowhere nearoptimal, which is particularly problematic for high throughputapplications such as those in the semiconductor industry.

At present, if the value of any one of the several manually selectedcontrol parameters is not at or within a reasonable range of itsoptimum, poor performance and unacceptable data will likely result. Inaddition, relatively complex interdependencies existing between certainAFM parameters often make setup a trial and error procedure, even forthe most experienced AFM operators.

In performing AFM setup, the values for several control parameters mustbe set along with feedback loop gains for different operational modesand other instances where setting up such gains is required. Setup musttake into account and configure for parameters such as scan size, pixelsper line, number of scan lines, scan rate, tip scanning speed,digital-to-analog (D/A) resolution, Z-center position, i.e., Z-centervoltage or the center of the Z piezo operation range, tip wear control,and sample damage minimization.

When an AFM is set-up to operate in an oscillatory mode, such as

TappingMode™, setup must include choosing an amplitude and setpointassociated with the oscillation. Moreover, initial values for integralgain (I-gain), and proportional gain (P-gain) are also manually set.Selecting gain values can be tricky because it typically depends onfactors such as the nature of the oscillatory mode being employed,sample topography, the hardness and/or roughness or any other mechanicalcharacteristics of the sample and medium in which it is located, as wellas other factors. For example, where gain is set too low, systemresponse tends to be relatively slow, which can result in the tip nottracking the sample surface. Where gain is set too high, the feedbackloop can start oscillating or backfeeding upon itself, which canundesirably add considerable noise to the sample image being generated.

In addition, the gain setup may be fine initially, only to be unsuitablelater once some other factor, such as topography changes. For instance,where the sample is relatively rough, gain typically should be sethigher in order to image such high featured topography with anyresulting increase in feedback oscillation noise being tolerable. Wherethe sample is relatively smooth or flat, gain should be set lower tominimize noise. By keeping noise low with low gain, better resolution offlat areas is achieved, thereby enabling the AFM to better image itsfiner details. However, as understood in the field, excessive noise canadversely affect imaging along flatter areas of the sample where aninitially high gain setting ends up being too high when the sampleflattens out. Conversely, an initial low gain setting frequently impedesimaging of higher features of the sample producing an image with suchhigher features being either distorted or missing.

These setup considerations become even more problematic when operatingin TappingMode™ because the highest useable gains typically depend oncantilever dynamics. Cantilever dynamics are a function of the free airtapping amplitude and setpoint and thus tuning the gains is verydifficult, especially for the novice user. Indeed, factors such ascantilever dynamics and Z-actuator response speed can create suchdifficulty in setting the initial setpoint and gains, the operator oftenresorts to trial and error until the sample image starts to look good.

Unfortunately, because one can affect the other, trial and error can goon for a long time. For example, as setpoint is lowered, gain can be sethigher and vice versa. However, while lower gains may permit a lowersetpoint to be used, which typically increases cantilever response, italso increases error generation rate, which can undesirably blur orotherwise distort the image being produced during scanning.

In the end, what often results is the operator setting some initialparameter values, gains and setpoint and then manually adjusting thevalue of each, one-by-one until feedback oscillation occurs and thenbacks off. While this process may work reasonably well for experiencedAFM operators, it is inefficient, time consuming, and quite often, lessthan optimal. In addition, it does nothing to address the dynamic natureof AFM imaging, which often requires an operator to either changecertain settings on the fly during operation or to observe the image,etc., and go back and re-scan those parts of the sample that are poorlyimaged with adjusted parameter values. Once again, this process can beextremely slow.

As a result, the field of scanning probe microscopy was in need of whatone might call a “point and shoot” solution for imaging and mechanicalproperty measurement on a wide array of samples that preferably is easyto use, as well as capable of minimizing the forces generated bytip-sample interaction while also maintaining fast imaging speeds.

SUMMARY OF THE INVENTION

The preferred embodiments take advantage of the new mode of AFMoperation known as Peak Force Tapping (PFT) Mode™ (PFT Mode andPeakForce Tapping Mode are trademarks of Bruker Nano, Inc., SantaBarbara, Calif.), in its design of a control scheme that minimizes theneed for a skilled and experienced user. PFT Mode essentially eliminatesthe need for the user to tune the gain while imaging. Moreover, PFT Modeenables further ease of use of an AFM by providing the ability toautomatically control operating parameters such as the setpoint, Z-limitand scan rate.

Fundamentally, the preferred embodiments are directed to an AFM thatlimits the need for an expert user and are realized by employing PFTMode which operates to move the tip substantially perpendicularly to thesample surface to cause the tip to interact with the sample, and thendepart from the sample. The feedback circuit uses instantaneousinteraction force (e.g., substantially orthogonal to the sample surface)at any interaction point, preferably using the maximum repulsive force.This new mode of operation takes advantage of the instantaneous responseof the probe upon tip-sample interaction (no need to wait for ring-downlike prior techniques, the present technique determines a baseline orzero force reference and forcefully substantially instantaneously bringsthe tip back to the surface), using the feedback loop to maintain asteady state interaction, and to control tracking of the tip on thesample. By moving the tip perpendicularly to the sample surface, thismode shares the advantages of TappingMode™ AFM to at least substantiallyeliminate friction forces during raster scanning or other relative probesample motion in the XY plane. In addition, the implementation of thismode minimizes parasitic coupling so that a far more sensitive forcecontrol than PFM and TappingMode™ AFM can be accomplished (at leastthree (3) orders magnitude). In doing so, the lowest force imaging(using alternating force) known in the AFM art is realized and directlycontrolled, thus allowing the AFM to provide improved high resolutionimages exceeding TappingMode™ AFM at speeds exceeding typicalTappingMode™ AFM speeds (TappingMode™ bandwidth is below 1 kHz).

An added benefit of PFT mode is that each cycle of the vertical movementproduces a force curve, or multiple force curves at each pixel, allowingsimultaneous acquisition and mapping of height and mechanical propertydata. This method is therefore called Peak Force Tapping (PFT) modesince it generates and analyzes each and every individual force curve,then measures and controls the AFM based on the corresponding peakinteraction forces during each instance of the tip tapping on thesample, with imaging speed higher than TappingMode™ imaging speed.

In accordance with a first aspect of the invention, a method ofoperating a SPM includes generating relative motion between a probe anda sample and detecting motion of the probe. The method recovers, fromthe detected probe motion, a probe-sample interaction that issubstantially independent of parasitic probe deflection (i.e., parasiticcantilever motion).

In another aspect of the invention, a method of operating a SPM includesgenerating an image while maintaining a maximum repulsive probe-sampleinteraction force of no more than about 10 pN during each cycle ofsubstantially perpendicular cyclical movement of the tip relative to thesample. Such interaction force can be directly controlled and accuratelycalibrated.

According to another aspect of the invention, a method of operating anSPM includes generating an image for at least 1 hour with peak force ofless than 5 nN, without user intervention, while maintaining an imageresolution better than 5 nanometers regardless of environment, includingambient, gaseous, fluid and vacuum.

In another aspect of the invention, a method of operating an SPMincludes generating at least one force-distance curve for each imagingpixel. The force-distance curve can be used to produce accuratemeasurement of one or more of van der Waals adhesion, elasticity, workof adhesion of tip-sample interface, plasticity such as hardness andviscoelasticity.

According to another aspect of the invention, the Peak Force Tappingmethod of operating an SPM includes using cantilevers with springconstants equal to about 0.01 N/m to 1000 N/m (which can enable thecapability to map mechanical properties over a range from about 10 kPato 100 GPa). This range of applicable cantilevers is several orders ofmagnitude wider than cantilevers generally applicable to ContactMode AFM(0.01-1 N/m) and TappingMode™ AFM (1 N/m-40 N/m).

A SPM configured in accordance with the invention could be used to scana wide variety of samples, including patterned wafers, biologicalsamples in ambient and fluid, polymers, thin films, and data storagedevice component.

According to a further aspect of the invention, a method of operating aSPM includes interacting a tip of a probe with a sample, thenterminating the interaction, resulting in a decaying probe oscillation.Thereafter, the method repeats the interaction before ring-down of thedecaying probe oscillation is substantially complete, and detects themotion of the probe.

In another aspect of the invention, a method of operating a scanningprobe microscope (SPM) includes generating relative motion between aprobe and a sample, and then detecting motion of the probe. In addition,the method includes recovering, from the detected probe motion, asubstantially instantaneous force between the tip and sample.Preferably, the method also automatically controls the generating stepto maintain a feedback setpoint.

In another aspect of the invention the control loop controls theinteraction force at a pre-determined synchronization distance.Synchronization distance is defined as the time from the start of amodulation period to the time corresponding to the point chosen tocontrol feedback. The instantaneous force occurring at this time pointis used as the feedback control parameter, usually chosen as the pointwhere the peak repulsive force occurs.

Again, Tapping Mode is complicated by a) indirect force control and b)cantilever resonance dynamics of multiple harmonics modes. Another majordrawback is that neither amplitude nor phase of the probe oscillationduring data acquisition has a monotonous relationship with tip-sampleinteraction force. As a result of these complications, subjectivejudgment must be employed in the feedback optimization process toacquire a desired image, which often means that the user must be an AFMexpert to achieve a high quality image, with minimal interaction force,and with the best stabilized (most robust) feedback. The synchronizedpeak force control of the preferred embodiments (PFT Mode) eliminatesthe complications due to cantilever dynamics, as well as thecomplications induced by cantilever resonance and its harmonics. Also,for the first time, PFT Mode uses interaction force directly as thefeedback control parameter. Even in contact mode AFM, constant drift ofthe cantilever deflection due to thermal or other system factors makesaccurate force control impossible. In Peak Force Tapping Mode, thesystem re-establishes the non-interacting baseline by moving the probefar from the sample in each interaction period. This process allowsaccurate determination of the interaction force every time the probeinteracts with the sample. Through direct force control and eliminationof the complications due to cantilever dynamics, the criteria requiredto achieve the highest quality images became monotonous. As a result,automation of the control loop can be implemented by designing anappropriate computer program. The subjective judgment of an expert user,based on her past experience of, for example, imaging a similar sample,to optimize feedback performance is also eliminated.

In yet another aspect of the invention, the automatically controllingstep includes automatically determining a minimum interaction forcerequired for control based on the noise background of the system. It isthis minimum interaction force that can be used as the setpoint in thecontrol feedback loop.

In yet another aspect of the invention, the automatically controllingstep includes determining feedback instability within less than 5tip-sample interaction periods (for example, 2.5 ms), about 100 timesfaster than an expert's visual judgment.

In yet another aspect of the invention, the automatically controllingstep includes automatically controlling a gain in a correspondingfeedback loop.

In a further aspect of the invention, the method includes automaticZ-limit control, and preferably automatic scan rate control.

These and other features and advantages of the invention will becomeapparent to those skilled in the art from the following detaileddescription and the accompanying drawings. It should be understood,however, that the detailed description and specific examples, whileindicating preferred embodiments of the present invention, are given byway of illustration and not of limitation. Many changes andmodifications may be made within the scope of the present inventionwithout departing from the spirit thereof, and the invention includesall such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred exemplary embodiments of the invention are illustrated in theaccompanying drawings in which like reference numerals represent likeparts throughout, and in which:

FIG. 1 is a block diagram of a conventional atomic force microscope,appropriately labeled “Prior Art”;

FIG. 2A is a graph of tip-sample separation versus time in oscillationAFM modes;

FIG. 2B is a graph of interaction force versus time in oscillation AFMmodes;

FIG. 2C is a graph of an SPM force curve illustrating probe sampleinteraction, “ring-down” and illustration of a second probe sampleinteraction;

FIG. 3 is a graph of force versus time illustrating determininginstantaneous force for feedback control according to the preferredembodiments;

FIG. 4A is a schematic graph illustrating probe deflection versus timeillustrating tip sample interaction force modulated periodically withparasitic oscillations in the system;

FIG. 4B is a schematic of cantilever probe response versus time withonly hydrodynamic background oscillation due to parasitic sources;

FIG. 4C is a graph of deflection error versus time after subtraction ofhydrodynamic background oscillation;

FIGS. 5A-5C is a series of graphs of a) deflection response beforebackground subtraction, b) the subtracted background and c) thedeflection error versus time after subtraction of hydrodynamicbackground oscillation;

FIG. 6A is a schematic illustration of force versus time illustratingthe baseline averaging method of the preferred embodiments;

FIG. 6B is a graphic illustration of tip-sample separation versus time;

FIG. 6C is a graphic illustration of cantilever deflection versus time;

FIG. 7 is a schematic graph of force versus time illustrating the priorart technique of averaging to a force over an entire cycle (RMS) todetect tip sample interaction;

FIG. 8A is a schematic force versus time curve illustrating the gatedaverage repulsive force control according to the preferred embodiments;

FIG. 8B is an illustration of an input synchronization signal sent withthe force response due to tip-sample interaction to realize gatedaverage repulsive force control according to the preferred embodiments;

FIG. 9A is a schematic illustration of a series of force curves used insynchronous averaging according to the preferred embodiments;

FIG. 9B is a graph illustrating a synchronization signal sent with thedeflection applied in the force curve of FIG. 9A;

FIG. 9C is a graph illustrating a force curve signal after severalcycles of synchronous averaging of FIG. 9A;

FIG. 10 is a schematic block diagram of an AFM operable in PFT Mode,according to one embodiment;

FIG. 11 is a flow diagram illustrating a method according to thepreferred embodiments;

FIG. 12A is a schematic graph of a force curve illustrating the systemsetpoint and measured deflection;

FIG. 12B is a schematic illustration of the feedback error producedaccording to prior art methods that control AFM operation by triggeringon force after completion of one modulation cycle;

FIG. 12C is a schematic illustration of the feedback error, similar toFIG. 11B, according to the preferred embodiments of the presentinvention;

FIG. 13 is a flowchart illustrating a method according to the preferredembodiments illustrating deflection background subtraction;

FIG. 14 is a flow diagram illustrating cantilever deflection backgroundsubtraction using a lock-in amplifier, according to the preferredembodiments;

FIG. 15 is a flow diagram illustrating deflection background subtractionin a normal engage process;

FIG. 16 is a flow diagram illustrating deflection background subtractionin a sewing engage process;

FIG. 17 is a graph of force versus time illustrating baselinecalculation according to the preferred embodiments;

FIG. 18 is a graph of force versus time illustrating an algorithm usedto determine instantaneous interaction force;

FIG. 19 is a flow diagram illustrating a method of instantaneous forcecontrol imaging;

FIGS. 20A and 20B are graphs illustrating force versus time and zposition respectively, when using instantaneous force control imagingaccording to the preferred embodiments;

FIGS. 21A and 21B are AFM images illustrating deep trench measurementsusing TappingMode™ AFM and instantaneous force control mode according tothe preferred embodiments;

FIG. 22A is a graph of force versus tip-sample separation, illustratingsmall amplitude repulsive force mode (SARF) according to the preferredembodiments;

FIG. 22B is a graph illustrating force versus time for the SARF mode;

FIG. 23A is a graph of force versus tip-sample separation, illustratingsmall amplitude attractive force mode (SAAF) according to the preferredembodiments;

FIG. 23B is a graph illustrating force versus time for the SAAF mode;

FIG. 24A is a schematic graph of feedback tracking signal versus scanposition showing a sample profile and the corresponding tracking signal(height) during AFM imaging, illustrating the difference between stableand unstable feedback;

FIG. 24B is a schematic graph the feedback error signal corresponding tothe height signal of FIG. 24A;

FIG. 25 is a schematic graph of spectrum amplitude versus frequency,illustrating a feedback signal spectrum which is used to detectinstability of the feedback loop according to a preferred embodiment;

FIGS. 26A-D is a series of schematic graphs illustrating parachutingdetection indicating that the tip-sample interaction force is at aboutthe baseline during a parachuting event;

FIG. 27 is a schematic diagram of an AFM according to the preferredembodiments, illustrating gain control in the feedback loop;

FIG. 28 is a schematic diagram of the oscillation detection algorithm ofFIG. 27;

FIGS. 29A-D is a schematic illustrations of the data re-sampled andprocessed by the oscillation detection algorithm of FIG. 28;

FIG. 30 is a diagram illustrating an implementation of a preferredembodiment of operating an AFM in PFT Mode;

FIG. 31 is a flow diagram of a scan rate control algorithm for use inPFT Mode;

FIG. 32A is a schematic graph of tip-sample interaction force when scanrate is substantially optimized;

FIG. 32B is a schematic graph of tip-sample interaction force when scanrate is not substantially optimized;

FIG. 33 is a diagram illustrating a method of Z-limit control accordingto a preferred embodiment; and

FIG. 34 is a schematic tip-sample interaction force diagram illustratingtip radius monitoring using the techniques of the preferred embodiments.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The preferred embodiments are directed to a Peak Force Tapping (PFT)Mode of AFM operation in which the interaction force between the probe(tip) and sample is monitored and used to control tip-sample separationat very low forces, yet without compromising scanning speed. Thetechniques described herein provide high resolution by maintaining probetip-sample forces low, and realizes essentially real-time propertymapping of sample surfaces. The preferred embodiments are inherentlystable and thus facilitate long-term force control while maintaining theability to acquire high integrity data (improved resolution). Moreover,because tuning is not required, unlike conventional TappingMode′ AFM,the AFM setup is faster and easier than with other AFM modes. The keyconcepts driving the PFT Mode are illustrated graphically and discussedherein.

Practically, there were three major issues to be resolved before AFMcontrol using instantaneous interaction force could be implemented.These issues were 1) accommodation of deflection background due tocoupling; 2) determination of a baseline; and 3) determination of theinstantaneous force, as defined herein.

In FIG. 2A, a cycle of modulation that approaches and separates theprobe from the sample (for example, using a drive to cyclically modulateprobe-sample separation) is represented by a period T. The zero position(horizontal axis) represents the surface while the vertical axis is theseparation. When the probe-sample separation crosses the horizontal zeroline, the tip is in direct contact with the sample, as represented byregion δT (the window of tip-sample contact). The interaction forcecorresponding to this region is plotted in FIG. 2B.

With further reference to FIGS. 2A and 2B, A_(max) is the maximumseparation of the tip apex from the sample; F_(a) _(_) _(vdw) is the vander Waals adhesion force; and F_(a) _(_) _(max) is the maximum adhesiondue to capillary interaction and work of adhesion between the tip andthe sample surface. Both repulsive force and adhesive force arecalculated relative to the baseline as shown in FIG. 2B. It should benoted that the force referenced here is the total force acting on theentire tip which is typically, pyramidal-shaped. In fact, the very apexportion can enter the repulsive zone while the total force remainsattractive. In this case, the feedback can still use the apex repulsiveinteraction force at the predefined synchronization position (defined asdiscussed below) for feedback, even though the total force at this pointis attractive. This provides the benefit of operating with the minimuminteraction force with the highest imaging resolution since the controlis determined by the apex repulsive interaction which arises from thePauli and ionic repulsions between the atoms of very apex of probes andthe atoms or molecular of samples.

It is important to differentiate cantilever deflection and tip-sampleinteraction force. While cantilever deflection is used to gauge thetip-sample interaction force, not all the deflection representstip-sample interaction force; namely, parasitic forces contribute tocantilever deflection. For example, as shown in FIG. 2C, the cantileverdeflection is plotted as a function of time, the figure representingactual deflection data. The oscillation after point “D” is due tocantilever free resonance decaying with time. This resonance deflectionis not caused by tip surface interaction and is considered a parasiticdeflection contribution (typically corresponding to parasitic cantileveror probe motion). Point E represents a maximum point of deflection atwhich the tip is not interacting with the sample. The “flat” portion ofdata also could have a slower variation of the deflection, when the tipis not interacting with the sample, typically caused by mechanicalcoupling of parasitic forces. Such coupling could be due to themodulation actuator itself, and/or cantilever response due to dampingforces from air or fluid. It can also arise from laser interference.These parasitic effects will be further illustrated in subsequentfigures.

In known force control systems, the control is based on a maximum forceoccurring in a period. Hence the repulsive force must be higher than anyof the parasitic contributions to deflection for true tip-sampleinteraction to be differentiated from parasitic forces and historicallyused by the feedback loop. This force differentiation requirementrequired a relatively high imaging force that could damage the tipand/or the sample, thereby preventing the system from achieving highresolution.

In a preferred embodiment, the RMS or constant deflection is replaced byan instantaneous interaction force F_(r)i, determined according to FIG.3, with the controller setpoint being:

δFr=F _(r) _(_) _(i) −F _(baseline)  Equation (1)

F_(baseline) is the interaction force when the probe is not contactingthe sample. It should be zero. In AFM, the force is usually representedby cantilever deflection. In this case, F_(baseline) corresponds to thecantilever deflection when the tip is not interacting with the surface.F_(r) _(_) _(i) is the interaction force when the tip is at closeproximate contact with the surface. A synchronization algorithm is usedto align the start time of each drive period, so that the region δT(FIGS. 2A-2B) coincides with the repulsive force and its maximum F_(r)_(_) _(max). The time from the start of the period to the occurrence ofthe F_(r) _(_) _(max) is the synchronization time, which can beprecisely determined and controlled (described further below).Synchronization time distance (Sync Distance) can be determined bymeasuring the phase delay between the deflection response and themodulation drive signal. Once the Sync Distance is determined (when theprobe is stationary in the xy direction), the same Sync Distance is usedthroughout all xy raster scanning positions. During imaging, thefeedback operates to maintain F_(r) _(_) _(i) substantially constantwhile the value of F_(r) _(_) _(i) is determined by the Sync Distance.Note that the Sync Distance can also be generalized as the distance fromthe starting of the modulation period to the instant of interaction.

The synchronizing distance or Sync Distance can be precisely controlled.For example, if the tip oscillation period T is 100 μs, when thesynchronizing distance is 48 μs, the interaction force occurring at the48th μs will be used as the feedback control parameter. The feedbackloop will try to maintain an instantaneous interaction force F_(r) _(_)_(i) (i=48 μs) at the 48th μs from the start of the period. In moregeneral applications, any point of interaction force within theinteraction region δT can be used for feedback. δT can also extendbeyond the marked region in FIG. 2B to include the region of F_(a) _(_)_(vdw) (van der Waals attractive region) and F_(a) _(—max) (thecapillary adhesive region). The capillary adhesive region can also beadhesive interaction due to bonding force induced by functionalizedprobes and specific bonds on the sample.

To achieve an accurate measurement of the baseline, multiple deflectiondata points are gathered when the tip is not interacting with the sampleand used to generate an averaged baseline level. Again, thenon-interaction region (greatest separation/highest distance) can bedetermined by the Sync Distance because this region should be around thehalf cycle of the modulation period after the peak force position. TheSync Distance also determines the feedback force operating point, andthe actual force is measured by δFr. δFr can be either negative orpositive.

Due to adverse effects of drift (e.g., thermal) on the deflectionsignal, the corresponding force F_(r) _(_) _(i) may vary over time. Therelative force δFr (relative to baseline determination) preferably isused for feedback control instead of F_(r) _(_) _(i) because it is amore accurate reflection of tip-surface interaction. This relative valueremoves the adverse influences due to system drift on cantileverdeflection.

δFr also represents a controllable force by the feedback loop such thatδFr remains constant over time at various positions as the tip scansacross the sample.

In FIG. 4A-4C, the cantilever response, when interacting with the samplesurface, is a mixture of the tip-surface interaction force and thebackground coupling. Such response is exhibited schematically in FIG. 4Aas “Original.” The real tip-sample interaction force is only at theF_(r) _(_) _(i) portion (shown in 4C), which is buried within thebackground of parasitic cantilever or probe motion. By subtracting thebackground from the original data (for example, probe motion includingdue to both interaction forces and parasitic forces), the magnitude ofthe interaction force can be obtained. The background, illustrated as4B, can be caused by mechanical coupling of resonances from the AFMsystem, and/or cantilever response to its environmental medium, such asair and fluid. It can also be induced by laser interference as thecantilever moves relative to the sample. The common characteristic ofthe background is that cantilever deflection displaying periodic changeis similar to the tip trajectory, even when the tip is not interactingwith the sample. A successful subtraction of background experimentaldata is shown in FIGS. 5A-5C.

More particularly, FIG. 5A shows a schematic illustration of theoriginal probe deflection versus time. As noted, the deflection of theprobe is highly influenced by parasitic sources that may be used tocontrol tip-sample interaction. As shown, these periodic parasiticdeflections are represented by the low frequency signal that we refer toherein as the “hydrodynamic background,” for example or parasitic forcein a more general term. The contribution to the probe deflection bythese parasitic forces (including hydrodynamic forces, drag forces andair, off-axis motions, laser inference and any other periodic motionoccurring when the probe is not interacting with the sample) is large.The actual tip-sample interaction force which should be used as thecontrol signal in the preferred embodiments is superimposed on theparasitic background signal (FIG. 5B), so it can be a challengedetecting the actual tip-sample interaction forces. Stated another way,the minimum controllable force is determined by the backgroundcontribution to probe deflection (shown in FIG. 5A as the Min.Controllable Force_(OLD)—range of about less than 1000 micro-newtons toless than 10 pico-newtons). Notably, as is always the case, a noisesignal “N” having a low amplitude relative to both the parasitic forcecontribution to the deflection and the contribution to the deflection bythe tip-sample interaction force, is present.

Turning to FIGS. 5B and 5C, one key concept to the present preferredembodiments is the subtraction of the parasitic background signal (FIG.5B) from the deflection signal, as noted, thereby lowering the minimumcontrollable force. The background signal is determined by increasingtip-sample separation sufficiently to a controlled distance so that theprobe does not interact with the sample, i.e., only parasitic forces arecontributing to the detected deflection of the probe. The controlleddistance is typically greater than 100 nm, though it can be less,ideally being a distance at which long range interaction forces do notcontribute to probe deflection. As shown in FIG. 5C, the tip-sampleinteraction force contribution to the deflection after subtracting theparasitic background renders a deflection signal having clear peaksassociated with the tip-sample interaction. Notably, the non-periodicnoise will always be present, and in this case, determines the minimumcontrollable force as shown in FIG. 5C (Min. Controllable Force_(NEW)).For a very soft cantilever with a spring constant of 0.01 N/m andcantilever length of 100 um, this force can be about 1 pN

It becomes clear that the minimum controllable force employable whenperforming parasitic background subtraction is lessened greatly (by, forexample, three (3) orders of magnitude), allowing the preferredembodiments to control tip-sample separation so the probe-sampleinteraction forces are reduced to the pN range. The way in which thissubtraction may be accomplished in the hardware is described furtherbelow with respect to FIG. 10.

In FIG. 10, “Z” represents a direction perpendicular to the samplesurface, indicating the vertical position between tip and samplesurface, generally referred as the tip position.

Overall, it is primarily this ability to detect such small forces, andto use such forces as a control parameter in an SPM feedback loop, thatallows an SPM operating according to the present invention to image asample using what is referred to herein as “instantaneous forcecontrol.” Instantaneous force control using real-time force detectionoffers improved control, thus improving image resolution and minimizingthe chance for sample damage. In this context, real-time orinstantaneous force detection implies that essentially each point of thevarying force illustrated, for example, in FIG. 3 can be detected by thepreferred embodiments and used instantaneously to control SPM operation.In other words, the varying forces acting on the probe due toprobe-sample interaction during each cycle of the interaction betweenthe probe and sample [or during each cycle of the modulation of theseparation between the two, i.e., the force curve modulation] aredetected and may be used by the AFM to image the sample in real-time.This instantaneous force control is used to provide AFM control at anyinteraction point within what would be one cycle of the modulation ofthe probe-sample separation. Because control is provided prior tocompletion of any would-be cycle of modulation (prior to the nextapproach), the feedback delay is greatly reduced. This will be shownfurther in connection with FIGS. 12A, 12B and 12C.

Yet another benefit in the peak force tapping control is that it doesnot need to be operated near the cantilever resonance frequency. Suchoperation can substantially eliminate cantilever delay due to transientresonance response, rendering instantaneous interaction controlpossible.

Turning next to FIG. 6, the preferred embodiments also allow the AFM tooperate at high speed by performing baseline averaging of the forcecurve to extract a zero force point quickly, and allow the system tocause the probe to interact with the sample with little time delay. Incontrast to prior techniques represented by FIG. 2C, the modulationfrequency of the present AFM is not limited by the requirement that thesystem wait to re-establish probe-sample interaction until probe“ring-down” completed (after the tip jumps off the sample surface, thedecaying of probe oscillation to about 1/e) to stabilize the imagingsystem. The time required for ring-down is determined by the cantileverdynamics which are proportional to Q/f, where Q is the quality factor ofthe cantilever and f is the cantilever resonance frequency—typicallytens of milliseconds for a conventionally used cantilever to stabilize.In the preferred embodiments, as shown in FIG. 6, upon ring-down, a fewcycles of the cantilever resonance frequency are averaged to determine azero force point (i.e., an at-rest baseline position) in essentiallyreal time, and allow the system to cause the probe to interact with thesample much quicker than the system illustrated in FIG. 2C. In fact, byconducting an average of even one cycle of the cantilever resonancefrequency upon ring-down, a robust estimation of the zero point(baseline) can be realized. As a result, modulation frequency can beincreased significantly without compromising system stability. Moreover,the added benefit of operating faster, of course, is reducing the effectof noise within the system.

For measurement with very sensitive force detection, very softcantilevers (spring constant 0.01 N/m to 0.3 N/m) are typically used.These levers have lower resonance frequency and very long ring-downtime. More importantly, the adhesion induced oscillation (snap out ofcontact) is much stronger, as shown in FIG. 6C. In FIG. 6C, thedeflection response of a soft cantilever is plotted as a function oftime. The tip trajectory is also plotted as a position reference (FIG.6B). As can be seen, the parasitic oscillation of the cantilever faroutweighs the interaction force, making control basically impossible.Previous to the present invention, a user would have to wait long enoughfor the oscillation to disappear so that F_(r) _(_) _(i) becomes theonly maximum, in order to have a steady control of the feedback. As thecantilever gets more sensitive, waiting for ring-down becomesprohibitively time consuming. The preferred embodiments of the presentinvention determine the baseline by separating the interaction zone andnon-interaction zone through synchronous alignment to the closestposition between the probe and the sample. A region corresponding to an“interaction zone” is locked through a synchronous marker, a referencetrigger signal at the beginning of each cycle. Any point of deflectionin this region can be used as the feedback parameter for steady stateinteraction control. All deflection data outside the interaction zoneare averaged to a constant and used as the baseline for calculatingΔF_(r) in FIG. 3. By combination of the baseline detection andsynchronous control, the relative force δF can be accurately determinedinstantaneously and controlled. Such control allows F_(r) _(_) _(i) tobe far below parasitic deflection, as illustrated in FIG. 6C.

Steady state again means a constant maximum force or a constant minimumforce, or a combination of the characteristics of the interaction forcecurve shape in each cycle of the probe/sample relative motion.

Another major advantage of the present techniques is the ability todetermine the baseline with high amplitude oscillatory data. Since theresonance frequency of the cantilever is known, in an alternativeembodiment, the average can be determined in the non-interacting zone byanalyzing an integer multiple of cycles of the cantilever resonancefrequency. The integer cycle averaging can effectively remove theoscillatory deflection data, yielding a constant baseline.

Notably, cantilever resonance frequency can also be determined by knowntechniques such as frequency sweep and thermal tune.

Turning next to FIGS. 7 and 8A and 8B, the preferred embodiments alsoemploy something referred to herein as “gated average repulsive forcecontrol.” FIG. 7 schematically shows probe deflection, including aseries of interaction periods, upon AFM operation. Prior controltechniques using force as a control parameter average the total forceover the entire cycle of tip-sample interaction, yielding an RMS valuefor comparison to the force setpoint. As understood in the art, theforces illustrated by the force curve are complex. Both repulsive andattractive forces operate on the probe tip during a cycle, as describedabove. By including, for example, the attractive force portion (C-D inFIG. 2C) which tends to cancel repulsive force, force sensitivity andimaging resolution are most often compromised.

Turning to FIGS. 8A and 8B, gated average repulsive force control isillustrated. In this embodiment, a system synchronization signal such asthat shown in FIG. 8B is used to “gate” the repulsive force portion (B-Cin FIG. 2C) of the force curve (illustrated by the shaded portion “A” ofthe deflection curve) by excluding the attractive force portion of theforce curve. By controlling tip-sample separation based on the repulsiveforce portion of the force curve, force sensitivity and imagingresolution are increased due to reducing the adverse effect of theattractive force portion of the curve (i.e., attractive interactionforces are long range interaction forces, and therefore senseinteraction over a much larger area, yielding lower resolution).Moreover, the gate operates to exclude the noise when performing thegated averaging. Again, the synchronization signal is timed so that onlythe repulsive force region is used. Such operation is ensured by usingthe gate at a pre-determined synchronization position as shown anddescribed in connection with FIG. 3.

Taking the above further, as shown in FIGS. 9A and 9B, synchronousaveraging can also be employed to further improve signal-to-noise ratio,and thus ultimately provide control at nearly the zero force point. FIG.9A, similar to the other tip-sample deflection illustrations, showsseveral cycles of deflection of the probe as the tip interacts with thesample. As noted previously, a noise signal is always present whenmaking these types of SPM/AFM measurements. By combining the deflectionsignal with a corresponding synchronization signal, such as that shownin FIG. 9B, synchronous averaging of the deflection is performed. As aresult, the effect of noise is reduced greatly according to,

$\begin{matrix}\frac{D_{1} + D_{2} + D_{3} + D_{4} + {\ldots \mspace{14mu} D_{N}}}{N} & {{Equation}\mspace{14mu} (2)}\end{matrix}$

Where D_(i) representing data in the ith cycle. The averaged signal witha signal to noise ratio improved by a factor of √N, thereby reducing theminimum controllable force (can use narrow lock-in bandwidth), is shownon FIG. 9C.

Turning next to FIG. 10, an AFM 100 operable in PFT Mode includes aprobe 102 mounted in a probe holder 108 and having a cantilever 104supporting a tip 106. In this case, tip-sample separation is modulatedby an actuator 112 (for example, an XYZ piezoelectric tube) coupled tothe probe holder 108 thereby. However, it should be understood that thepreferred embodiments are applicable to those AFM instruments thatmodulate tip-sample separation by moving the sample in Z.

During operation, probe deflection is measured by bouncing a light beam“L” off the back of the probe and toward a detector 114, such as a fourquadrant photodetector. The deflection signal is then transmitted to ananalog to digital converter 103. The digitized signal is used formaintaining the tip-sample force low while operating the AFM at highspeed.

In the embodiment shown in FIG. 10, probe deflection without tip-sampleinteraction is transmitted to a background generator 105. The backgroundgenerator will create a periodic waveform corresponding to thebackground signal when the tip and sample are not interacting. Thiswaveform can be generated by a DDS (Direct Digital Synthesis functiongenerator) whose amplitude and phase are determined by a lock-inamplifier, and whose input is the background signal. This waveform canalso be generated by synchronously averaging multiple cycles of thebackground with the help of a synchronization signal. A comparatorcircuit 120 processes the total deflection signal by subtracting thebackground signal so as to generate a signal representative oftip-sample interaction force independent of the parasitic background(FIGS. 4C and 5C). (Note that, though analog or digital circuitry may bedescribed, it is understood that the operations may be performed in anyconventional analog or digital circuitry, though a preferred embodimentutilizes FPGA architecture to implement the invention). This signal isthen fed through a digital filter 122 that processes thepost-subtraction deflection error to limit the processed ring-downoscillation of the lever to a number of selected cycles. The filteredsignal is transmitted to synchronous averaging circuit 123 to furtherincrease the signal to noise ratio. By averaging data in thenon-interaction region with the help of synchronization, a baseline isdetermined from baseline averaging circuit 124. A comparator circuit 125processes the total deflection signal by subtracting the baseline signalso as to generate a signal representative of tip-sample interactionforce with no cantilever DC drift. This signal is further transmitted toa force detector 126.

Sync Distance calculator 135 determines the phase shift between thedeflection and the Z modulation DDS (Block 127) that provides the driveand synchronization control in the form of a time delay. Peak force orrepulsive force gate position generator 129 generates the timing signalfor force detector 126, with the help of the synchronization marker andsynchronization time distance. Force detector 126 analyzes the output ofsummation circuit 125 by either identifying the repulsive peak force oraveraged repulsive force within the gated region illustrated in FIG. 8A.Again, by operating force detector 126 this way so force control can betriggered on a selected part of the force curve (e.g., repulsive forceregion), higher sensitivity is achieved by reducing the effect of theattractive force between the sample and tip. Moreover, signal to noiseratio is improved by excluding noise from the gate of detector 126. Thegated repulsive force is then compared to an appropriate setpoint (Block128), and an error signal is generated and transmitted to a controlblock (e.g., a PI controller 130). The control signal is then convertedto analog (converter 132) and transmitted to a summing circuit 134 forcombination with a synchronization signal from Block 127 after thesynchronization signal is converted to analog with a converter 136. Theoutput of summing circuit 134 is then applied to the Z-piezo 112 foractuating the z position (in this case, the probe) to maintainessentially steady state interaction between the tip and sample. Acorresponding method of operation is described in further detail belowin connection with FIG. 13.

Turning to FIG. 11, a method 300 of operating an AFM according to PFTMode is shown. After a setup and initialization Block 302 (no tuningrequired), the probe is driven into oscillation and engaged with thesample. Preferably, in Block 304, relative XY motion between the probeand sample is initiated (scanning).

Motion of the probe is then detected; in particular, probe deflection isdetected and transmitted to the converter for further processing. InBlock 306, the method then operates to recover probe-sample interactionas described above, preferably performing hydrodynamic backgroundsubtraction using either lock-in amplification, or more preferably,synchronous averaging of the deflection. After filtering the output inBlock 308 (e.g., selecting a number of cycles of ring-down to process),the method detects the force (peak force detection/gated averaging),preferably using the repulsive region of the force curve, in Block 310.In Block 312, the force is then compared to the setpoint force, setaccording to the user's desired interaction force. The Z-actuatorresponds to the control signals in Block 316 to adjust tip-sampleseparation and maintain the setpoint force, with the control signalsbeing used to generate an image of the sample.

Turning to FIGS. 12A-12C, an illustration of the ability of thepreferred embodiments to provide instantaneous force feedback is shown.In FIG. 12A, several schematic force versus time curves are shown withdifferent peak repulsive forces. Notably, interactions Q and S exceedthe threshold force defined by the setpoint, while interaction Rillustrates a peak repulsive force below that of the setpoint. Thefeedback error is illustrated as shown in FIG. 12B for prior art forcefeedback systems. More particularly, once the repulsive force exceedsthe setpoint, a delay “d” is shown prior to mapping peak repulsive forceat X for the first interaction. This is similar for the interactionlabeled S in which the feedback error is not established until wellafter the point at which the repulsive force begins to exceed thesetpoint.

To the contrary, as shown in FIG. 12C, the response to any force largerthan the setpoint is detected essentially instantaneously, given lessfeedback delay due to the features of PFT Mode discussed above,including parasitic background subtraction, baseline averaging and gatedaverage, repulsive force control, preferably in combination withsynchronous averaging. By being able to quickly identify forces abovethe setpoint, the forces corresponding to tip-sample interaction can beminimized, thus providing a significant advantage in terms of AFMoperation at high speed and high resolution. And this is especially truefor rough samples in which sample surface changes can limit responsetime and/or resolution.

Algorithms

To assure accurate subtraction of the background, two schemes have beendeveloped, as shown in FIG. 13 and FIG. 14.

In FIG. 13, an algorithm 400 for the subtraction of cantileverdeflection background (parasitic contributions to deflection) is shown.Blocks 402 and 404 assure the tip is far enough away (30 nm, forexample) from the sample so that there is no repulsive impulseinteraction on the surface, according to a user selection upon set up.Block 406 contains several sub-steps. The AFM system samples cantileverdeflection data for multiple cycles and digitizes the data into multiplesegments with each segment having a period T. The AFM method aligns eachsegment of data to the start of the period T, and then averages thedata. Next, method 400 uses the averaged segment data as the backgroundfor the period T. Block 408 operates to subtract the background obtainedfrom Block 406 from the measured data in each period T using, forexample, an FPGA processor. Block 408 uses the background corrected datafor feedback.

In FIG. 14, another algorithm 500 for subtracting background deflectionis shown. Blocks 502 and 504, calculating lift height and lifting thetip with z feedback off, are used to ensure the tip is not interactingwith the sample. Block 506 uses a lock-in amplifier with the drivesignal moving the cantilever probe as the reference, and the cantileverdeflection data as the lock-in input. In Block 508, the amplitude andphase data obtained from lock-in are used to construct a sinusoidalsignal, and this signal is adjusted and used to subtract the deflectiondata until deflection becomes a constant (within the noise limit). Realtime subtraction is performed in Block 510. Once sufficient subtractionis achieved (determined using a constant deflection when the tip is notinteracting with the surface), the AFM is able to use the backgroundcorrected data for feedback in Block 512.

The background calculated according to FIGS. 13 and 14 variessubstantially as the probe approaches the sample surface. Such variationis caused by hydrodynamic force as a function of the probe to samplesurface distance. Such variation can also serve as an indicator of thecloseness of the probe to the sample before it actually interacts withthe sample. With this knowledge, the motorized engaging can proceed at afast speed until a pre-defined background value is reached; slowerengage steps can then be performed.

Background subtractions are preferably also executed during engagementof the probe with the sample surface, as shown in FIGS. 15 and 16.

The difference between the two engage methods is that the “normal”engage 600 in FIG. 15 uses a step motor only to drive the probe towardthe sample to detect the sample surface. However, FIG. 16 shows a“sewing” engage that moves the probe with the Z-piezo at each motor stepas the method 700 searches for the sample surface. Referring initiallyto FIG. 15, method 600 initially steps, in Block 602, a motor to reducetip-sample separation according to a fixed step of, e.g., 0.1 nm toabout 3 microns. With feedback control on (force detection according tothe present techniques), the feedback loop controls the actuator to movethe tip, in this case, toward the sample in Block 604. In Block 606, thealgorithm determines whether the surface has been detected (i.e.,whether the threshold setpoint force has been reached). If not, abackground subtraction operation as described above in connection withFIG. 5 is performed prior to further stepping the motor in Block 602. Ifso, feedback is disengaged, and a lift height is computed by calculatingthe z movements between peak force and maximum negative adhesion forceposition, plus a certain margin (for example, 10 nm), and the tip can beraised in Block 610 (e.g., to minimize the chance of crash). Thereafter,in Block 612, a background subtraction operation is performed, andfeedback control according to the present techniques is again initiatedin Block 614.

In FIG. 16, Blocks 708, 712, 714 and 716 correspond directly with Blocks606, 610, 612 and 614 of the algorithm 600 of FIG. 15. However, prior todetecting the surface, a sewing engage such as that known in the art isemployed to lift the tip in Block 702 prior to stepping the motor downin Block 704; in this case, the lift is 1.5 times the motor step. Theamount of lift may be user-selected based on type of sample, etc.Thereafter, feedback is turned on in Block 706 to detect force accordingto the present techniques. If the surface is not detected, the algorithm700 performs a background subtraction in Block 710 (similar to Block608) prior to conducting another lift in Block 702. Once the surface isdetected, the SPM can image the sample in Block 716.

FIG. 17 illustrates a practical situation of the tip-sample interaction,and provides a supplemental discussion to the above in connection withFIG. 6. The real tip-sample interaction occurs only in the vicinity ofthe Sync Distance marker. In the interaction free region there is aresidual self-oscillation of the cantilever due to break-off of theadhesion force (aka, ring-down). Such oscillation causes baselinefluctuation, rendering the same fluctuation of δFr shown in FIG. 3. Suchvariation will become controller noise. In order to minimize baselinefluctuation, the data marked as within the “baseline average” region areaveraged into a single constant, represented by the dashed line. Thisconstant data is used as the baseline in calculating δFr in eachfeedback cycle. The region for “baseline average” can vary depending onthe data quality. It needs to be smaller than the Sync Distance to avoidaveraging the real tip-sample interaction occurring at about the SyncDistance.

The instantaneous interaction force can be determined by using the forceδFr calculated by Equation (1), in which F_(r) _(_) _(i) can be aninstant value at the Sync Distance. As illustrated in FIG. 18, it canalso be a value determined through a gated average (see also FIGS. 7 and8A/8B). The gated average scheme uses the deflection values in the timezone δt and averages all data points in this time zone. Doing so cansubstantially improve signal to noise ratio. F_(r) _(_) _(i) serves asthe setpoint in feedback control. It can vary from a value causingnegative δFr to a high positive δFr. A high positive number for δFrmeans stronger repulsive interaction with the sample.

FIG. 19 illustrates a procedure 800 of instantaneous force control usedfor Peak Force Tapping (PFT) imaging. In Block 802 an actuatoroscillates the probe or the sample, producing relative motion with anamplitude in the range of, for instance, 0.1 nm to 3 μm, peak-to-peak.At this point, the tip is not touching the sample, and a baseline andbackground can be determined in Blocks 804 and 806. Once the backgroundis determined, it is also subtracted from the detected deflection inBlock 806 to insure the minimum detectable force is as small aspossible. Block 808 operates to interact the probe with the sample by anengage, as detailed in FIGS. 15 and 16. Once the sample is interactingwith the probe, the deflection data in a period T is sampled anddigitized to analyze Sync Distance (FIG. 18), instantaneous force F_(r)_(_) _(i) and relative force δFr in Block 810. The baseline andbackground can be re-checked according to FIG. 14 at this Block.

Feedback is then used to maintain δFr and F_(r) _(_) _(i) at the presetvalue in Block 812. The XY scanner is also enabled, Block 814, toreposition the probe relative to the sample and eventually generate atopographic image, as well as one or more mechanical images indicativeof, for example, elasticity, adhesion, and energy dissipation.

In FIG. 20 the time resolved measurement curve in FIG. 20A is convertedto real space data in FIG. 20B. More particularly, FIG. 20A is a plot ofthe interaction force as a function of time in one modulation period.FIG. 20B is the interaction force as a function of tip-sample distancein one modulation period. The elastic property of the material can becalculated conventionally by using the upper part of the slope (seesegment DE in FIG. 20B, segments CDE illustrate short range repulsiveinteraction) using, for example, the Oliver-Pharr model, or anothercontact mechanical model. (see, e.g., Oliver W C and Pharr G M 2004Measurement of Hardness and Elastic Modulus by Instrumented Indentation:Advances in Understanding and Refinements to Methodology J. Mater. Res.19 Mar. 20, 2004). The van der Waals attraction force can be determinedfrom the approaching curve (segment BC in FIGS. 20A and 20B), whilecapillary adhesion, which occurs when the tip departs from the sample,can also be calculated. (see, e.g., “Theoretical Investigation of theDistance Dependence of Capillary and Van der Waals forces in ScanningForce Microscopy”, Stifter et al., Physical Review B, Vol. 62 No. 20,Nov. 15, 2000). By moving the tip in the xy-plane and repeating thesemeasurements, sample properties such as elasticity, van der Waalsadhesion and capillary adhesion (segment EF corresponds to attractionand capillary forces) can be imaged for the entire sample surfaceregion, or some part thereof. Furthermore, from the difference of theapproaching curve and retrieving (departing) curve, the hardness of thesample can also be imaged.

FIG. 20B represents two types of data, namely direct measurement dataand derived data. Direct measurements data are parameters, such asinteraction force that are determined instantaneously within each cycle.The derived data are calculated data within each interaction cycle fromany part of the curve. Such data can be deformation, which is calculatedby the penetration depth from point C to point D in FIG. 20B. Anotherexample is the dissipation energy defined by the area enclosed in theapproaching curve (BCD) and withdraw curve (DEFG). Yet another exampleis the adhesion force calculated through the difference between B and Fin FIG. 20B. Any of the derived data can be used as the feedback controlparameter. For example, when the deformation is chosen as the feedbackparameter, the control loop in FIG. 1 will produce an image based on aconstant deformation, instead of constant peak force. Any other deriveddata can serve the same purpose in the feedback loop.

One important application of the instantaneous force controlled imagingis in deep trench measurement. When TappingMode™ AFM is used to imagedeep trenches (aspect ratio of about 3:1 or more, with the mostdifficult trenches to image having sub-100 nm width, typically 10 nm-100nm) the strong attractive force at the side walls can cause amplitudechange, resulting in a false measurement of the trench depth. Usingdirect repulsive force as feedback, the feedback only responds toz-change when the tip is in contact with the sample. As a result, theforce controlled feedback can measure deep trenches much more reliablythan TappingMode™ AFM. FIGS. 21A and 21B provide a demonstration of thismeasurement. The measurement uses the same probe and sample at the samesample location. The instantaneous force control feedback loop was ableto give a real trench depth measurement with the tip reaching the trenchbottom (FIG. 21B). TappingMode™ AFM, on the other hand, moved the tipprematurely, yielding a much shallower depth measurement and no trenchbottom was measured (FIG. 21A).

Referring finally to FIGS. 22A/22B and 23A/23B, additional features ofthe present invention are described. In FIGS. 22A and 22B, the AFM isoperated to modulate Z at an amplitude small enough (e.g.,sub-nanometer) to make sure that tip-sample interaction always stays inthe repulsive force zone (Small Amplitude Repulsive Force Mode), i.e., afew nanometers away from surface. This is accomplished by using eitherpeak-to-peak force difference (F_(a)-F_(b), corresponding to thepeak-to-peak Z modulation), or amplitude output of a lock-in amplifier,as feedback. The feedback parameter is proportional to the repulsiveforce gradient if the amplitude is small enough in which case the forcegradient is linear. In this case, feedback is only sensitive to shortrange chemical bonding forces, forces corresponding to atomicresolution. As a result, the present technique is ideal for highresolution imaging.

In FIGS. 23A and 23B, a similar arrangement to that shown in FIGS.22A/22B is shown, but the attractive force portion of the force curve isemployed (Small Amplitude Attractive Force Mode). In this case, thesystem modulates Z at an amplitude that is small enough to make suretip-sample interaction stays in the attractive force zone all the time.Again, either simple peak-to-peak force difference (F_(a)-F_(b)), oramplitude output of a lock-in amplifier, can be used as feedback giventhat the feedback parameter is proportional to the attractive forcegradient if the amplitude is small enough so that the force gradient islinear. This technique is the least destructive to the sample since thetip does not make contact with the sample. In comparison to the SmallAmplitude Repulsive Force Mode, the feedback polarity is inversed.

Advantages—PFT Mode

The primary benefits of PFT Mode AFM operation are: 1. Improved imagingstability. 2. Higher resolution with less damage to tip or sample. 3.Higher tracking bandwidth or higher imaging speed. 4. Direct physicalquantity measurement capability. 5. Reliable fluid imaging. 6. Abilityto choose from a wide range of cantilever types to accommodate a widerange of samples and applications. 7. Ease of use.

In sum, the benefits of PFT Mode AFM operation are numerous. Thebenefits listed above are from the application point of view. Thesebenefits are a reflection of the advances in the operation mechanism.

Improved imaging stability: Given the inherently stable long term forcecontrol, drift-free sample imaging can be achieved along withsimultaneous height, stiffness, adhesion, elasticity and plasticitymechanical property measurements at TappingMode™ speeds. Because thetechnique is not impacted by DC drift (PFT mode creates its ownreference every few hundred microseconds), steady operation is achievedeven without an expert operator. This allows continuous imaging forhours or even days (large samples-long time) without substantiallycompromising image integrity. The benefit of imaging stability isparticularly useful for in-process measurements, like crystal growth andmonitoring polymer phase change, which can take several minutes or evenhours.

Higher resolution with less damage to tip or sample: When compared toexisting modes of AFM operation, the low force high speed imagingprovided by PFT Mode in combination with the low average tracking forceand the virtual elimination of lateral forces on the tip, provide asignificant advance in high speed imaging over a wide variety ofsamples. For example, single molecule elasticity can be measured, aswell as narrow DNA samples in fluid (e.g., 2 nm wide DNA). Bycomparison, when imaging DNA in fluid, TappingMode™ AFM has at least a 2nm lower resolution. Moreover, measuring DNA stiffness in fluid ischallenging with TappingMode™ AFM because it does not have propertyquantification capacity, it primarily is only able to provide relativemechanical property measurements (for example, by looking at contrast inphase images). With the present technique, property measurement down tothe molecular level can be achieved.

Compare to TappingMode™, PFT Mode can acquire data with higherresolution (e.g., a resolution less than a 100 nm, and more preferablyless than about 1 nm laterally) and less tip-sample force (i.e., lessdamage to the tip and/or the sample). The technique provides significantspeed improvement over other known force feedback techniques and does sowithout requiring the use of a small lever. In fact, a rather largelever (>60 μm long) can be operated at sub-resonance in PFT Mode so thatthe lever response has a bandwidth far beyond that achievable when usinga so-called small cantilever (>10 kHz).

An additional benefit of the present preferred embodiments is that aforce curve is generated at every pixel so that the image providesinformation beyond a typical TappingMode™ AFM image. With every pixel,the user can obtain quantitative information regarding stiffness,adhesion, elasticity, plasticity, etc. And again, because baselinetip-sample separation is calibrated at every pixel, drift is minimizedso that a large improvement in productivity and image reliability isrealized.

Higher tracking bandwidth or higher imaging speed: Notably, a Peak ForceTapping image can be generated at an operating bandwidth greater than 2kHz. Conventional Tapping Mode bandwidth is about 1 kHz, primarilybecause of the slow cantilever dynamics (slow response of cantileveramplitude to the change in tip-sample distance).

Direct mechanical property measurement capability: The disclosedembodiments independently measures elasticity, adhesion, energydissipation, etc. All these factors contribute to the phase ofcantilever oscillation. Therefore although phase channel is employed torepresent the mechanical property information in TappingMode™ AFM,ambiguity remains in the interpretation of the measured phase. PFT Modeeliminates the phase interpretation problems by providing directmechanical property measurement.

Ability to choose from a wide range of cantilever types to accommodateto wide range of samples and applications: PFT Mode is insensitive tocantilever dynamics because the measured peak force is not limited bycantilever dynamics. This allows for high speed imaging in vacuum, airand fluid.

Typically, TappingMode™ AFM require cantilevers to have spring constantsgreater than 0.3 N/m, while PFT Mode can use cantilevers having springconstants as low as 0.01 N/m. Again, this is due to the fact that PFTMode does not depend on the oscillation energy stored in the cantileverto overcome capillary adhesion forces. Because the technique utilizes anexternal actuation element (of the feedback circuit, preferablytriggering on peak force), the mechanism to overcome the capillaryforces is far more powerful than in TappingMode™ wherein the staticelastic energy of the cantilever itself (fed by the kinetic energy ofthe oscillating probe) pulls the tip away from the sample in overcomingthe capillary forces. As a result, there is virtually no limitation onthe cantilever spring constant to operate stably in the presence of acapillary layer. PFT Mode therefore enables stable tapping controloperation using a cantilever having a spring constant at least as low as0.01 N/m.

PFT Mode allows using cantilevers from 0.01 N/m to 1000 N/m in one modeof AFM operation. It enables high resolution mechanical property mappingof the broadest range of materials (from 10 kPa to 100 GPa in elasticmodulus) on a single instrument.

Reliable fluid imaging: The fact that PFT Mode does not have to operateat the resonance frequency of the probe offers a major advantage whenimaging in fluid. Due to various parasitic coupling forces in fluid,cantilever tuning is a difficult step in the success of obtaining aTappingMode™ fluid image. PFT Mode completely removes the need to tunethe cantilever (baseline averaging, background subtraction, etc.).Furthermore, the range of force control and the ability to choose acantilever from a much wider spring constant range gives imaging controlmuch more room for biological sample imaging.

Ease of use: In addition, given essentially instantaneous forcefeedback, tip crashing is virtually eliminated. Also, because thedeflection is dynamically corrected, no tuning is typically required,and therefore fast, ready setup by virtually any user can beaccomplished.

In review, the present PFT Mode provides very low force imaging toprovide very high resolution using real time property mapping (i.e.,instantaneous force control). The force control is inherently stable(essentially drift free), over a term sufficiently long to image asample with minimal or no user intervention. The system allows faster,simpler set-up because no tuning is required (baseline averaging andhydrodynamic background correction). Moreover, precise control overforce basically eliminates tip crash, while the technique/system alsoessentially eliminates lateral force on the sample surface. The systemis also insensitive to cantilever dynamics by not having to wait forprobe ring-down before interacting the probe with the sample. And, asdiscussed, a wide range of cantilevers are available to the user toobtain simultaneous measurements of height, stiffness, adhesion,elasticity and plasticity at TappingMode™ AFM speeds (>2 kHz). Thepresent PFT Mode can image samples such as 2 nm wide DNA in fluid withthese characteristics, as well make improved mechanical propertymeasurements such as single molecule elasticity.

PFT Mode—Ease of Use

The preferred embodiments of the present invention use PFT Mode to allowa novice user the ability to produce high quality images with qualitysimilar to that of an expert user. In contrast to TappingMode™ AFM whichoperates by controlling tip-sample interaction based on deviations from,for example, a setpoint amplitude or phase of probe oscillation as thetip interacts with the sample (representing a complex relationshiprelative to tip-sample forces), PFT Mode controls tip-sample interactionbased on tip-sample interaction forces at each point along a cycle ofprobe modulation. This direct control of the interaction forcesimplifies the control and allows the preferred embodiments to minimizethe effects of complicating variables, including the dynamics of thecantilever and other mechanical components including the actuator, andthus maintain stability.

FIG. 24A shows a schematic graph 1000 of a sample profile (height) 1002including rising regions 1004 and falling regions 1006. Superimposed onthis profile 1002 is a tracking signal or image 1008 obtained by an AFM.As a scan continues in the indicated direction, stable feedback ismaintained. Stable feedback refers to a feedback loop that does not tendto be self-excited, i.e., generate oscillatory output regardless ofinput. At point “X”, however, the feedback begins to become unstable,and the image starts to appear noisier. By decreasing feedback gain(s),unstable feedback may become more stable (at a cost—reduced imagingbandwidth, or imaging speed, etc.). FIG. 24B is an error signalcorresponding to the superimposed tracking signal 1008. Importantly,both the height signal and the error signal of the unstable feedbackappear noisier than those of the stable feedback. This phenomenon willbe utilized in the automatic gain scheduling apparatus and method of thepresent invention described below.

FIG. 25 illustrates conceptually, using a plot of an amplitude spectrumof the feedback height or error signal, feedback instability detectionused by the preferred embodiments. Signal spectra are shown for bothstable feedback 1010, and unstable feedback 1012. The feedbackinstability can be quantitatively measured based on one or more ofseveral criteria. A few examples of these criteria are: 1. the spectrumamplitude at a certain frequency (f₀). Frequency f₀ is determined usingsystem identification or from observing the spectrum of the feedbacksignal when the feedback is unstable. 2. the RMS error of height orerror signal. 3. The standard deviation of height or error signal.

Turning to FIGS. 26A-D, an illustration of tip-sample force when the tiploses contact with the sample (also known as “parachuting”) is shown.Similar to FIG. 24A, FIG. 26A illustrates a schematic diagram 1020showing a sample profile 1022 as well as an AFM tracking (height) signal1024 superimposed thereon. In this case, in the region marked “A”, thetip loses contact with the sample surface during the image scan and isparachuting as the control system attempts to return the tip to thesample surface (typically by moving either the probe or the sample).FIG. 26B shows that, on downward sloping surfaces (1026 in FIG. 26A, forinstance), the error signal (the difference between measured tip-sampleinteraction force and the setpoint) goes negative, causing the controlsystem to attempt to move the tip toward the sample. In flat regions(1032), the error is zero such that the tip is tracking the surfacewithout correction. On upward sloping surfaces (1030), the error ispositive and the control system uses this information to attempt to movethe tip away from the sample. In the parachuting region “A” however(corresponding to downward sloping portion 1028 of the sample), theerror first indicates a downward sloping portion, but because thefeedback is unable to follow the fast descending slope the tip stopstracking the surface as the tip-sample interaction force goes to zero(see FIG. 26C).

During parachuting the tip-sample interaction force is not related tothe tip-sample distance. Therefore, during parachuting, feedbackstability is compromised. It is important that the parachuting event isdetected so that gain scheduling is disabled during the period ofparachuting. A method to detect parachuting using PFT Mode is describedbelow.

FIG. 26D, showing a zoom on the tip-sample interaction force data,illustrates force curves corresponding to regions of tip-sampleinteraction (where feedback correction is required). A zoom in for anindividual tip-sample interaction force curve is shown in FIG. 20A. Theinteraction force can be characterized by an attractive region BC (snapto contact—van der Waals forces), a repulsive region CDE as the tipinteracts with the surface and continues its cycle of oscillation, anadhesive region EF as the tip attempts to pull away from the surface,and then a point F at which it releases. One advantage of PFT Mode over,for instance, TappingMode™, is that every point on the interaction forcecurve can be used by the controller to track the surface (withoutwaiting for ring-down prior to driving another cycle of modulation), asdiscussed at length previously. In the case of a parachuting tip,parachuting can be detected in the presently preferred embodiments byone or more of the following criteria: 1. peak force/adhesion force orpeak-to-peak force within an oscillation period is less than a thresholdvalue. 2. feedback error signal is between two threshold valuesindicating the peak force is near zero. 3. standard deviation and/orspectrum amplitude at a certain frequency (or frequencies) of feedbackerror signal is less than a threshold value indicating the feedback loopis open.

An AFM 1100 operable in PFT Mode to minimize the skill required tooperate the AFM is shown schematically in FIG. 27. AFM 1100 includes aprobe 1102 including a cantilever 1104 supporting a tip 1106. Probe 1102is mounted in a probe holder 1108. In this case, probe holder 1108 iscoupled to an actuator 1110. Actuator 1110 (such as a piezoelectricactuator) can move tip 1106 of probe 1102 in “Z” direction (orthogonalto the sample surface). As the probe 1102 interacts with the sample1109, its deflection is monitored by a deflection detection scheme 1112including a light source 1114 (e.g., a laser diode) that directs a beamof light “L” towards the backside of the lever 1104. Lever 1104 reflectsthe beam “L” towards a detector 1116 (e.g., a quadrant photodetector)that transmits a signal indicative of deflection toward an ADC 1118.After the analog deflection signal is converted to digital by ADC block1118, the resultant signal is transmitted to a PFT Mode Force Detectionblock 1120. The detected force signals (determined according to theabove-described apparatus and methods for extracting tip-sampleinteraction forces point-by-point) are transmitted to a comparisoncircuit 1122. Preferably, the peak force is compared to the forcesetpoint, and the error signal is sent to a PI controller 1124. PIcontroller 1124 outputs a control signal that is transmitted to a Z ScanDAC block 1126 that converts the digital signal to an analog signal,which is further applied to the Z piezoelectric actuator 1110 to controltip-sample separation. The above mentioned components form a feedbackloop, so that the interaction force between tip 1106 and sample 1109 isregulated according to the force setpoint.

In operation, the Z Scan control signal output by DAC 1126, andoptimized by gain control circuit 1123, is combined with the output ofthe Z offset DAC 1136 (described further below) and the oscillatingdrive for PFT Mode provided by a Z modulation DDS (direct digitalsynthesizer) 1138 at summing circuit 1139.

To facilitate stability, and thus minimize the need for an expert user,the gain is automatically tuned using a gain control circuit 1123. Thecontrol signal from PI Controller 1124 used to control the Z piezo 1110is also transmitted to a block 1128 that re-samples the height data at aposition corresponding to, preferably, the peak force (see block 1120).An oscillation detection algorithm 1130 is then employed to determinewhether there is oscillation in the height data, i.e., whether there isan onset of instability. If the system is about to oscillate and becomeunstable, high frequency noise will be detected. The way in whichalgorithm 1130 determines the amount of noise is described in furtherdetail below in connection with FIG. 28. Oscillation detection algorithm1130 outputs a signal indicative of the magnitude of the instability,short termed “noise” only for this section. Such instability exhibitsitself like noise and is caused by the feedback loop. But it should notbe confused with noise in other parts of the system when feedback is notturned on. This noise signal is compared to a noise tolerance margin atsumming circuit 1132. The noise tolerance margin is a predeterminedparameter associated with the product and it can be further optimizedafter initiation of imaging according to sample roughness informationacquired during scanning. For example, the noise tolerance can bereduced if the sample is determined to be very flat. If the error outputof circuit 1132 exceeds the predetermined margin, gain controller 1134determines an appropriate gain control signal to adjust the gains ofcontroller 1124 by, for example, reducing I gain and P gain in smallsteps (5%, each iteration, for example) until the magnitude of theinstability signal out of oscillation detection algorithm 1130 becomesless than the noise tolerance margin. In sum, at each imaging location,the gain may be optimized to ensure system stability.

With this automatic gain scheduling active, the need of expert usertuning of the gains during AFM operation is eliminated.

One of the critical elements in automated adjustment of feedback gainsis the ability to determine instability onset quickly and accuratelyduring scanning. This determination is often complicated by unknowntopography which may be misinterpreted as the instability induced noisein the gain controller. Turning to FIG. 28, an algorithm 1140 forimplementing oscillation detection block 1130 of FIG. 27 is described infurther detail. Height information is used to determine the level ofinstability oscillation because the height is calibrated on any AFMsystem and is independent to any system specific parameters such asscanner Z range and cantilever deflection sensitivity, etc. A noisetolerance margin (Block 1155) is defined as the allowed magnitude ofinstability induced noise. When this margin is detected using the heightsignal, such margin provides an absolute value of noise allowed in thefeedback system. For example, if the noise tolerance margin is 1 nm, anyinstability output from Blocks 1146 or 1148 is considered acceptable.For a sample height of 100 nm (range), such margin corresponds to asignal to noise ratio of 100 in the image. However for flat sample withcorrugation less than 1 nm, the noise tolerance margin will be largerthan the sample height signal. In such a situation, the noise tolerancemargin should be reduced to 0.1 nm to get a reasonably good image(S/N=10). This margin can be self-adjusted based on the sampleroughness. The height data obtained during AFM operation reflects bothsample topology and system oscillation. In general, algorithm 1140operates to filter out sample topology in order to determine whether thenoise is sufficiently large to indicate an onset of instability. It isimportant to know that, during scanning, the sample topology usuallydoes not have large changes in adjacent pixels. By calculating theheight difference between, for example, three (3) adjacent points, thesample topology can be largely filtered out. This is shown usingfollowing equations:

Assume the height of 3 consecutive pixels around location x₀ is

$\begin{matrix}{{{H\left( {x_{0} - {\Delta \; x}} \right)},{H\left( x_{0} \right)},{H\left( {x_{0} + {\Delta \; x}} \right)},{so}}{{H\left( {x_{0} + {\Delta \; x}} \right)} = \left. {{H\left( x_{0} \right)} + \frac{dH}{dx}} \middle| {}_{x = x_{0}}{{\Delta \; x} + \frac{d^{2}H}{{dx}^{2}}} \middle| {}_{x = x_{0}}{{\Delta \; x^{2}} + \frac{d^{3}H}{{dx}^{3}}} \middle| {}_{x = x_{0}}{{\Delta \; x^{3}} + \frac{d^{4}H}{{dx}^{4}}} \middle| {}_{x = x_{0}}{{\Delta \; x^{4}} +} \right.}} & (3) \\{{H\left( {x_{0} - {\Delta \; x}} \right)} = \left. {{H\left( x_{0} \right)} - \frac{dH}{dx}} \middle| {}_{x = x_{0}}{{\Delta \; x} + \frac{d^{2}H}{{dx}^{2}}} \middle| {}_{x = x_{0}}{{\Delta \; x^{2}} - \frac{d^{3}H}{{dx}^{3}}} \middle| {}_{x = x_{0}}{\Delta \; x^{3}\frac{d^{4}H}{{dx}^{4}}} \middle| {}_{x = x_{0}}{{\Delta \; x^{4}} +} \right.} & (4)\end{matrix}$

add equation 3 to equation 4, we have:

$\begin{matrix}{{H\left( {x_{0} + {\Delta \; x}} \right)} = {{H\left( {x_{0} - {\Delta \; x}} \right)} = \left. {{2{H\left( x_{0} \right)}} + {2\frac{d^{2}H}{{dx}^{2}}}} \middle| {}_{x = x_{0}}{{\Delta \; x^{2}} + {2\frac{d^{4}H}{{dx}^{4}}}} \middle| {}_{x = x_{0}}{{\Delta \; x^{4}} +} \right.}} & (5)\end{matrix}$

So

$\begin{matrix}{\frac{\left( {{H\left( {x_{0} + {\Delta \; x}} \right)} = {{H\left( {x_{0} - {\Delta \; x}} \right)} - {2{H\left( x_{0} \right)}}}} \right)}{2} = \left. \frac{d^{2}H}{{dx}^{2}} \middle| {}_{x = x_{0}}{{\Delta \; x^{2}} + \frac{d^{4}H}{{dx}^{4}}} \middle| {}_{x = x_{0}}{{\Delta \; x^{4}} +} \right.} & (6)\end{matrix}$

with a small position change Δx, the height difference will be small.

In this regard, referring to FIG. 29, one example of the height controlsignal output by PI controller 1124 (FIG. 27) is shown on A. In thiscase, feedback loop is stable between t1 and t2. It starts to oscillatefrom t2 to t5. Referring back to FIG. 28, the height data is re-sampledin Block 1142. Re-sampling in this context means extracting the heightdata points at, preferably, a peak force position of at least threeadjacent force curves. In Block 1144, a difference in height between aselected number of data points or pixels is determined. For example, ifthree points are chosen, the calculation becomes,

H Diff(i)=(H(i−1)+H(i+1)−2*H(i))/2  Equation 7

The result of this operation is shown on FIG. 29C. The topology data islargely filtered out with just very little leftover, but oscillationdata during t2 and t5 basically unchanged. As shown on FIG. 29D, theabsolute value of this difference |H Diff(i)| indicates how stable thefeedback is at certain time. Referring to FIG. 28, this is done in Block1146. This step operates essentially like an oscillation detector. Then,in Block 1148, a moving average may be determined. By determining amoving average of height differences, which are computed over relativelylong periods of time, a baseline of how stable the feedback loop isestablished. Determining a moving average is only required for thosesamples that exhibit significant changes in topology such that thetopology might not be filtered out in a given sample used for the heightdifference calculation. Such samples include, for example, a silicongrating with sharp steps. In such cases, the rapid change in topologyresults large spikes in the height difference output data. Since thosespikes are typically short lived, by compare them to the moving averageof height difference data with the operation shown on FIG. 28, Block1149, those spikes will be totally removed. On the other hand, if thereis an oscillation, because problematic oscillation noise typically lastsmuch longer than topology changes, the associated height difference datatends to be similar to previous moving averaged data and so isessentially passed by.

Continuing with method 1140, in Block 1149, if the absolute value of thedifference obtained in Block 1146 is less than some multiple of themoving average, for example, four (4) times the moving average valuecomputed in Block 1148, the output of oscillation detection algorithm1140 is |H Diff(i)|. If the absolute value of the difference is greaterthan the multiple, then the output of algorithm 1140 is the movingaverage value. The RMS value of this quantity is then determined inBlock 1150. It is this value that is compared to the “Noise ToleranceMargin” by summing circuit 1152, described above in connection with FIG.27. Finally, gain control feedback (increase/decrease the gain) isdetermined and transmitted to PI controller 1124 based on the erroroutput of circuit 1132 in Block 1154. Gain is increased if the output of1130 is lower than Noise Tolerance Margin 1155. Gain is decreased if theoutput of 1130 is higher than the Noise Tolerance Margin 1155.

A particular implementation of AFM operation using PFT Mode isillustrated in FIG. 30. To take advantage of PFT Mode and make theinstrument user friendly, automatic gain scheduling control (herein alsoreferred to as “auto pilot” or “auto piloting the AFM”) as describedabove is implemented as follows. The user defines a desired scan size inBlock 1502. An engage routine is then initiated in Block 1504, bringingthe tip and sample into contact. The AFM system then determines whether“auto piloting” is on in Block 1506. If not, this routine is complete(Block 1530) and the AFM operates using operator controlled feedbackwithout auto gain control (some expert users may prefer to monitor theirmeasurement and make manual gain and setpoint adjustments). If autopiloting is on, operational parameters are initialized in Block 1508through factory defined default values, as is the DSP in Block 1510.Block 1512 indicates that auto pilot function is implemented in the DSP.

Once the parameters are initialized, scan size is set to a small valuein Block 1514. A small scan (10 nm, for example) is performed at lowgain to determine an initial peak force setpoint and gain to provide asetpoint reference. For all AFM imaging, minimizing the peak tip-sampleinteraction force generally leads to improved tip life and sampleintegrity. The system can determine the minimum setpoint based on theknowledge of the base noise in the system. For example, if the forcedetection noise, when the tip is not interacting with the sample, is 100pN, the setpoint may be set at 300 pN, allowing enough signal to noiseratio for feedback control. In Block 1516, the engage is verified, andin Block 1518, the system modifies the initial gain and setpoint in anattempt to optimize the same. The optimization is an iterative processincluding,

-   -   1. Determining system background noise by lifting the tip so        that there is no tip-sample interaction;    -   2. Determining a setpoint, usually three (3) times higher than        the peak force noise background determined in Step 1; and    -   3. Increasing the gain (iteratively, in predetermined steps, for        example) until the noise is about equal to the noise tolerance        margin.

Once the gain and force setpoint are determined at small scan size inBlock 1520, the system restores the user-input scan size in Block 1522and begins AFM operation to acquire sample data.

In Block 1524, the system determines whether the algorithm is adjustingthe gain or setpoint. If either gain or setpoint is not being adjustedby the algorithm, the default gain/setpoint value is restored in Block1526. The system then enters a monitoring loop (Monitoring Mode) inBlock 1528. Monitoring Mode determines whether oscillation exceeds thethreshold. If so, gain can be adjusted (decreased). If not, gain can beincreased for better tracking. Monitoring Mode also operates to detect aparachuting event. If a parachuting event is detected as describedabove, the setpoint may be increased for optimal performance. Setpointincrease is implemented, preferably, by 5% increments each time (andoptionally verifying steps 1-3 outlined above). The above continuesuntil the scan of the user-defined sample scan size is complete.

It is important to point out that the relative position between theprobe and the sample represents two distinct concepts. Since the tip ismoving periodically, the position of the probe at any instant isreferred to as the probe position. The averaged position in one periodof the motion is the mean probe position. For example, if the probe ismoving sinusoidally with the angular frequency of “w” and amplitude of“a” the probe position at any instant is a*sin(wt). However the averageposition of the probe is zero since the average in one sine cycle iszero.

The Z position controlled by the feedback loop provides control of themean position.

In sum, the above-described feedback control is able to maintain asubstantially identical peak interaction force in each modulation periodof probe oscillation/tip-sample interaction. The method automaticallydetermines a setpoint associated with the peak interaction force basedon noise background, and automatically determines feedback gainaccording to an oscillation magnitude of the instability. By doing so,the AFM can be used by a novice user to obtain images with selfoptimized gain and setpoint value.

In contrast to Tapping Mode the nature of the feedback in PFT Mode isconsiderably different. In most AFM control schemes, the feedback loopis implemented using integral and differential gain control, or simply aP/I feedback loop. Feedback is driven by the difference between a presetvalue (set point) and the current value of peak force. This differenceis also called the error signal, as described earlier. The P/I feedbackloop is a linear compensator. It has the most predictable behavior ifthe error signal to be compensated for using feedback is also linearlyvarying with the tip-sample interaction. The peak force errorintrinsically is linear in nature because such error grows linearly withtip-sample interaction. This linearity of the error is the key elementfor achieving automatic tuning of P/I gain (also called gainoptimization) with long term robustness over a broad range of samples.

The gain optimization described in FIGS. 28 and 30 operates to increasegain to the highest bandwidth for fastest feedback response, and thusfaster imaging.

Setpoint optimization mean a process described in FIGS. 28 and 30 tominimize the interaction peak force, therefore the setpoint value neededto track the surface.

Scan rate optimization means automatically adjusts scan speed so thatthe scan rate allows the setpoint to operate with a predefined margin(peak force error), while achieving highest possible scan rate. Forexample, if the setpoint margin is 10 nN, the automatic gain adjustmentand setpoint adjustment will work on any optimized value with the peakforce below 10 nN. If setpoint adjustment at 10 nN is insufficient tomaintain stability the automatic control in FIG. 30 will decrease thescan rate to assure the largest peak force error is within 10 nN.

The scan rate can be automatically adjusted for optimization using PFTMode, as shown in FIG. 31. In FIG. 31, a flow chart of a scan controlalgorithm 1600 is shown. In this case, the AFM is operating in PFT modein Block 1602, which includes continuous monitoring of the peak force ineach cycle of tip-sample interaction. In Block 1604, method 1600determines whether that peak force is greater than a preset threshold.For example, the threshold may correspond to a measurement greater than8 volts. If so, a scan rate adjustment signal is transmitted to thescanner to reduce the scan rate by an appropriate amount in Block 1608.If not, then the method determines whether the background change isgreater than a particular threshold (for example, 0.25 volts) in Block1606. If so, scan rate is reduced in Block 1608. If not, the currentscan rate is maintained in Block 1610. This optimal scan rate controlcan be optimized at every pixel when operating in PFT Mode. PFT Modethus strikes the ideal balance between acquiring high quality images inthe shortest amount of acquisition time. To further explain block 1606,as an example, referring to FIGS. 32A and 32B, FIG. 32A illustrates flatbackground regions on either side of a cycle of tip-sample interactionforce. In FIG. 32B, the background is affected by changes in sampletopography—the tip maybe stuck in the sample due to it not being able totrack the surface. In this case, this background change is identifiedand used to slow the scan.

PFT Mode also enables automatic Z-limit control, further facilitatingease of use of this AFM. The Z-limit parameter defines the dynamic rangeof the Z piezo actuator. Preferably, the probe is centered in thisrange. Larger Z-limit allows imaging of a sample having large topographyvariations, but at the same time reduces the bit resolution. For certainflat samples, the Z-limit needs to be adjusted in order to acquire ahigh resolution topography image. Previously, Z-limit adjustment wasbased on the user's experience. In PFT Mode, control of the Z-limitparameter is automated. In this regard, turning to FIG. 33, after method1700 initiates operation in PFT Mode in Block 1702 (Z-limit is set toallow maximum Z range), method 1700 captures one complete frame of thesample surface corresponding to the scan area defined by the user inBlock 1704. The RMS height of the frame is then computed in Block 1706.If the RMS height is less than a threshold (e.g., 10 nm), as determinedin Block 1708, then the Z-limit is adjusted in Block 1710. For example,for a flat sample that meets the threshold, the Z-limit may be reducedto a particular value, 2 microns for instance, and the frame re-scanned.This may be done iteratively until the user is satisfied with the imageand moves on. Preferably, the adjusted Z limit is maintained until theuser changes the scan area.

In addition to automation, PFT Mode is useful for maximizing the abilityto insure quality imaging and obtain mechanical property measurements ofthe sample at every scan location (e.g., pixel) of the sample. Forinstance, PFT Mode can be used to perform tip radius monitoring. Onemajor setback to obtaining high quality images is the difficulty of theuser to detect when the sharp probe tip has been compromised. The tipmay be compromised due to contamination (materials from sample orenvironment attach to the tip, which often occurs when imaging in fluidor imaging an oily sample, for example) and/or from the change in thephysical structure (part of the tip fractures or wears out). Acompromised tip can be identified by reviewing a force curve obtained ata sample location. FIG. 34 illustrates the portion of the force curveindicative of tip health. In FIG. 34, schematic graph 1801 representstip trajectory. This trajectory can be part of a sinusoidal signal andan arbitrary shape defined using the scanner control signal. Atpositions close to sample van der Waals attraction force is plotted assegment A-B in schematic graph 1802 where 1802-1 represents thenon-interacting zero force baseline. The slope of this segment isdetermined using tip radius. A larger tip radius will cause point A tomove left, corresponding to an earlier onset of van der Waals force. Byanalyzing segment A-B, one can estimate tip radius and make a judgmentregarding whether the tip is still sharp. In particular, the slope ofregion A-B provides an indication of a tip artifact (the dashed lineschematically illustrating the response when an artifact is present).Because in PFT Mode one or more force curves are generated at each andevery pixel, tip force monitoring can occur substantiallyinstantaneously during the scan. Therefore, rather than interruptingimaging and obtaining a test force curve to try to identify whether thetip is compromised, the AFM operating in PFT Mode is able to identifysuch a condition automatically at every scan location (every few hundredmicroseconds, for instance). If identified, the scan can be discontinuedand the user notified, thereby preventing acquisition of further uselessdata and allowing the user to replace the compromised tip.

Another indication of tip health is contamination. Such contamination isdetermined by analyzing the shaded area “w” in schematic graph 1803 inFIG. 34, which is known as the work of adhesion. Work of adhesion ishigher if the tip is contaminated by water, or another substance, whichmay form a meniscus when the tip retracts from the surface. Larger workof adhesion represents more severe contamination. Since the force curveis acquired at each pixel, the health of the tip related tocontamination can also be continuously monitored.

If the tip is functionalized through chemical bonds with certainchemical components, such as Polyethylene glycol (PEG) or Dendron, thework of adhesion is then purposely introduced. In this case, thefunctionalized tip only generates significant work of adhesion when thechemical components interact with molecular sites that exhibitparticular interactions, for example, generate bonds to Polyethyleneglycol (PEG) or Dendron. By monitoring this interaction, the adhesionmap may become a chemical or biochemical recognition map.

One can also apply electric, optical, magnetic or thermal perturbationor excitation that is synchronized to the contact point D in schematicgraph 1802 of FIG. 34. Synchronous detection of current, voltage,thermal property, magnetic response or optical spectroscopy response canachieve substantial signal to noise improvement since point D representscontrol at near sample interaction (or near field interaction).

Advantages—PFT Mode and Ease of Use

In sum, PFT Mode provides several operational advantages that enableAFMs to be operated by non-expert users. When considering ease of use,several imaging factors must be accounted for to minimize the need foran expert user. First, stability of the feedback must be maintained and,with the above-described automatic gain tuning/scheduling enabled by PFTMode, stability is realized without any expert being present to manuallyadjust the gains. Next, to obtain quality images, the AFM must track thesample surface. By basing control on the instantaneous tip-sampleinteraction force, the setpoint force can be selected for optimumtracking with minimum error. Also, scan rate and auto Z-Limit control,as described above, also work to minimize the need for an expert whenoperating the AFM without compromising imaging speed or the ability toobtain high quality images.

In contrast to known oscillatory modes of AFM operation such asTappingMode™, PFT Mode operates in an entirely different dynamic regime.Oscillation mode setpoint is, typically, an amplitude or phase of theoscillation, a parameter that has a highly complex relationship with theinteraction and the force between tip and sample. As discussed herein,PFT Mode considers each point of tip oscillation as the tip interactswith the sample surface and uses the corresponding force information inits feedback scheme. This allows the preferred embodiments to operatewithout user controlled feedback, with no user adjustments beingrequired during imaging (auto-minimization of the error signal). PFTMode also provides intermittent contact with the sample (and itsunderstood benefits) with tuning (only requiring a simple pre-imageroutine—FIG. 30), and allows set-up without tuning. As a result, thenovice can image below a certain resolution (for example, 1 nN) andabove a certain speed (e.g., ½ Hz, 256 pixels) without having to do atune.

Moreover by providing a force curve at every pixel, the user is able toobtain deterministic data (e.g., adhesion) at a reasonable speed and ata certain resolution, and can do so while imaging. This is all enabledby feeding back directly on force (tip-sample) which allows responsebased on a single interaction between the tip and sample (representing alinear transfer function—direct contrast to known oscillating modes).

Notably, all the above concepts can be employed in the electricalcontext as well (e.g., STM) whereby the instrument feeds back oncurrent.

Also, because of the complex nature of the feedback, the data obtainedin conventional oscillating modes typically requires complex indirectinterpretation. PFT Mode allows direct interpretation of the data giventhat it is force curve based rather than tapping “envelope” based.

Another benefit of operating in PFT Mode includes the ability to imagecertain samples more effectively. For instance, in semiconductorapplications, the inability of AFM to reliably image narrow trenchesoften causes users wanting to perform such measurements to selectmetrology instruments other than AFM. However, in PFT Mode, peakinteraction force is used as direct force feedback and the tip is incontact with the sample in every force curve, thus enabling confidentmeasurement of high aspect ratio sample features.

In addition, PFT Mode is not subject to control parameter drift. Forexample, TappingMode™ AFM free amplitude may change during imaging dueto either the drive amplitude drift in air or the fluid cell driveefficiency drift in liquids, causing change in the tip/sample force, andmay result in loss of tip/sample interaction. Such drift preventsTappingMode™ AFM to perform long time stable imaging. With PFT Mode, auser can image for more than an hour (including overnight) versus lessthan an hour using conventional oscillating AFM modes especially inliquid environments.

Overall, in PFT Mode, there is a de-coupling of the cantilever responseto environmental conditions. Imaging in vacuum (fluid) and atmospherecan be accomplished without affecting set-up thus making the instrumentvery easy to use. The oscillation frequency can be set independent ofany cantilever resonance—greatly simplifying use in fluid. Inparticular, known intermittent contact modes require operation atresonance, while PFT Mode preferably operates at sub-resonance. This,again, is due to the ability to control based on ultra smallinstantaneous (not average) forces (about 1 μN to 1 pN). As a result,the AFM can also run feedback faster given that cantilever Q isirrelevant at subresonance (the transfer function is independent of theenergy store in the cantilever at resonance). Finally, PFT Mode alsoallows use of cantilevers having sub 1-10 N/m spring constants, asdiscussed above.

Although the best mode contemplated by the inventors of carrying out thepresent invention is disclosed above, practice of the above invention isnot limited thereto. It will be manifest that various additions,modifications and rearrangements of the features of the presentinvention may be made without deviating from the spirit and the scope ofthe underlying inventive concept.

1. A method for determining an occurrence of parachuting of a probe of ascanning probe microscope operating in an oscillating mode, the methodcomprising: providing relative motion between a probe and a sample andcontrolling that motion using a feedback loop that generates a feedbackerror signal in peak force tapping (PFT) mode; detecting at least one ofa peak force, an adhesion force and a peak-to-peak force on the probe;and determining one of a group including: a) whether the peak force, theadhesion force or the peak-to-peak force within an oscillation period ofthe relative motion is less than a threshold value, b) a point at whichthe feedback error signal is between two threshold values indicating thepeak force is about zero, and c) whether the standard deviation and/orspectrum amplitude, at a certain frequency or selected frequencies, ofthe feedback error signal is less than a threshold value which indicatesthat the feedback loop is open.
 2. The method of claim 1, furthercomprising, after determining an occurrence of parachuting, returningthe probe to the sample by moving at least one of the probe and thesample.
 3. The method of claim 2, further comprising moving the probetoward the sample when the feedback error signal is negative.
 4. Themethod of claim 1, further comprising, after determining an occurrenceof parachuting, disabling an automatic gain control for maintaining aninteraction between the probe and the sample during the period ofparachuting.
 5. A scanning probe microscope (SPM) comprising: anactuator that generates relative motion between a probe and a sample;and a controller configured to control that motion using a feedback loopthat generates a feedback error signal in PFT mode, wherein thecontroller detects at least one of a peak force, an adhesion force and apeak-to-peak force on the probe, and wherein the controller determinesone of a group including: a) whether the peak force, the adhesion forceor the peak-to-peak force within an oscillation period of the relativemotion that is less than a threshold value, b) a point at which thefeedback error signal is between two threshold values indicating thepeak force is about zero, and c) whether the standard deviation and/orspectrum amplitude, at a certain frequency or selected frequencies, ofthe feedback error signal is less than a threshold value which indicatesthat the feedback loop is open.
 6. The scanning probe microscope ofclaim 5, wherein, after determining an occurrence of parachuting, thecontroller returns the probe to the sample by moving at least one of theprobe and the sample.
 7. The scanning probe microscope of claim 6,wherein the controller moves the probe toward the sample when thefeedback error signal is negative.
 8. The scanning probe microscope ofclaim 5, wherein, after determining an occurrence of parachuting, thecontroller disables an automatic gain control for maintaining aninteraction between the probe and the sample during the period ofparachuting.
 9. A method of operating a scanning probe microscope (SPM),the method comprising: providing relative motion between a probe and asample; and detecting a parachuting probe relative to the sample whilecontrolling the motion in PFT mode.
 10. The method of claim 9, whereinthe detecting step includes determining when a feedback error signal isless than a threshold value.
 11. The method of claim 10, wherein thedetermining step includes using one of a standard deviation and aspectrum amplitude at at least one frequency of the feedback errorsignal.
 12. The method of claim 9, wherein the detecting step includesdetermining when at least one of a group including peak force, adhesionforce, and a peak-to-peak force within an oscillation period is lessthan a threshold value.